Measure of two sides of triangle is 10 and 14

Triangles are not classified by the length of their sides, but by their shapes. A right triangle, for example, is a triangle which includes one 90o angle. This is true regardless of the size of the triangle; it could have sides a thousand miles long or a thousandth of an inch long and still be a right triangle, as long as it has that 90o angle. An equilateral triangle has three sides which are all of the same length. This is true, again, regardless of the size of the triangle. The three sides could all be a million miles long, or they could be microscopic, but if they are all the same length, then the triangle is equilateral.It would be better to ask about classifying triangles by the relative lengths of their sides.If all the sides are different lengths, we class it as a Scalene Triangle. (Note that all three angles also are different.)If exactly two sides have the same length we call it an Isosceles triangle (Note that two of the angles also are the same size. And try to get the spelling right!!!)If all three sides are the same length, we call it an Equilateral triangle. (If you like you could say that it is a special case of an isosceles triangle). All three angle are the same and they always are sixty degrees each.

Question 23 Exercise 10.1

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Answer:

Solution:

Let the length of the third side be x cm.

The length of the other two sides is 12 cm and 14 cm.

Now, the Perimeter of triangle = 36 cm

12+14+x=36

26+x=36

x=36-26=10

Thus, the length of third side is 10 cm.

Video transcript

Hello students, welcome to the Lido learning. So here the question is two supplementary angles are Phi x minus 82 degrees + 4 x + 73 degrees. So here we have to find the value of the X. So let us write it starts the answer. So here solution is supplementary angles are 180 degrees, right? So here the equation is 5X minus 82 degrees plus 44 x + 73 degrees is 180 degrees. So you're freaking observe 9x minus 9 9 x minus 9 is equal to 180 degrees. So 9 x if we sent to the right-hand side we get 9x is equals to 1 89. So here if we send mine from multiplying to the right-hand side dividing. Sorry. Sorry. Sorry dividing X equals to one eighty-nine by nine is equal to the answer the final answer we get the x value is 21 degrees. Thank you for watching our video. A subscriber to our Channel and feel free to ask doubts in the comment section below. Thank you.

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To use the right angle calculator simply enter the lengths of any two sides of a right triangle into the top boxes. The calculator will then determine the length of the remaining side, the area and perimeter of the triangle, and all the angles of the triangle.

How to Find the Area and Sides of a Right Triangle

Do it yourself

If we know just two sides of a right triangle, we can use that information to find the third side, the area and perimeter of the triangle, and all the angles of the triangle. Amazing, right? Let’s review how we would find each of those parts.

How to find the Missing Side of a Right Triangle

To find the missing side of a right triangle we use the famous Pythagorean Theorem.

We need to be a little careful that we know which side we’re finding. Right triangles have two legs and a hypotenuse, which is the longest side and is always across from the right angle. When we’re trying to find the hypotenuse we substitute our two known sides for a and b. It doesn’t matter which leg is a and which is b. Then we solve for c by adding the squared values of a and b and taking the square root of both sides. 

When we’re trying to find one of the legs we enter the known leg for a and the known hypotenuse for c. Then we solve for b using simple algebra (subtract the value of a squared from both sides, then take the square root of both sides). 

How to find the Area of a Right Triangle

To find the area of a right triangle we only need to know the length of the two legs. We don’t need the hypotenuse at all. That’s because the legs determine the base and the height of the triangle in every right triangle. So we use the general triangle area formula (A = base • height/2) and substitute a and b for base and height. So our new formula for right triangle area is A = ab/2. 

How to find the Perimeter of a Right Triangle

To find the perimeter, or distance around, our triangle we simply need to add all three sides together. If we only know two of the sides we need to use the Pythagorean Theorem first to find the third side. 

How to find the Angles of a Right Triangle

To find the angles of a right triangle we use trigonometry. It’s not as difficult as it sounds. We just need to find one special button on our handheld calculators. To start we’ll need to know all the side lengths, so if we don’t know them already we’ll use the Pythagorean Theorem to find them first. 

Once we have all the sides we determine which angle we’re going to find. Then we take the side opposite that angle and divide it by the length of the hypotenuse, which is side c. That will give us a value between 0 and 1. Now we just need to find the ARCSIN button on our calculator, which is often labeled as SIN-1.  Finding the ARCSIN of our decimal value gives us our angle. Be sure that the calculator is set for angle mode rather than radian mode. 

We can repeat this process to find the other unknown angle in the triangle by once again dividing its opposite side by the hypotenuse and then taking the ARCSIN. 

Or we could show off even more triangle knowledge by using subtraction to find it since we know the interior angles of a triangle have to add up to 180°. Subtracting the angle we just found from 180° and then subtracting our known right angle (90°) will give us the third angle too. 

This calculator is great for getting all this information from just two sides of a right triangle, but it’s a fun challenge to try to find the sides, angles, area and perimeter on our own without it. Then you can use it to check our answers.

The right triangle calculator will help you find the lengths of the sides of a right-angled triangle. This triangle solver will also teach you how to find the area of a right triangle as well as give plenty of information about the practical uses of a right triangle.

First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°.

In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The relationship between the hypotenuse and each of the cathetus is a very simple one, as we will see when we will talk about Pythagoras' theorem.

If all you want to calculate is the hypotenuse of a right triangle, this page and its right triangle calculator will work just fine. However, we would also recommend to use the specific tool we have developed at Omni Calculators: the hypotenuse calculator. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².

To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula". A Pythagorean theorem calculator is also an excellent tool for calculating the hypotenuse.

Let's now solve a practical example of what it would take to calculate the hypotenuse of a right triangle without using any calculators available at Omni:

1. Obtain the values of a and b,
2. Square a and b,
3. Sum up both values: a² + b²,
4. Take the square root of the result,
5. The square root will yield a positive and negative result. Since we are dealing with length, disregard the negative result,
6. The resulting value is the value of the hypotenuse c.

Now let's see what the process would be using one of Omni's calculator, for example, the right triangle calculator on this web page:

1. Insert the value of a and b into the calculator
2. Obtain the value of c immediately
3. As a bonus, you will get the value of the area for such a triangle.

We have seen already that calculating the area of a right angle triangle is very easy with the right triangle calculator. At Omni Calculators, we have a calculator specifically designed for that purpose as well: area of a right triangle calculator. There is even one for the adventurous amongst you that would like to calculate the area of any triangle: area of a triangle calculator. Let's now see a bit more in-depth how to calculate areas of right triangles.

The method for finding the area of a right triangle is quite simple. All that you need are the lengths of the base and the height. In a right triangle, the base and the height are the two sides which form the right angle. Since multiplying these to values together would give the area of the corresponding rectangle, and the triangle is half of that, the formula is:

area = (1/2)base * height.

If you don't know the base or the height, you can find it using the Pythagorean theorem. Use the right triangle calculator to check your calculations or calculate the area of triangles with sides that have larger or decimal value length.

Now we're gonna see other things that can be calculated from a right triangle using some of the tools available at Omni. The sides of a triangle have a certain gradient or slope. We can use a slope calculator to determine the slope of each side. The formula for the slope (in case if you want to calculate by hand) is

slope = (y₂ - y₁)/(x₂ - x₁)

So if the coordinates are (1,-6) and (4,8), the slope of the segment is (8 + 6)/(4 - 1) = 14/3. An easy way to determine if the triangle is right, and you just know the coordinates, is to see if the slopes of any two lines multiply to equal -1.

There is an easy way to convert angles from radians to degrees and degrees to radians with the use of the angle conversion:

• If an angle is in radians - multiply by 180/π,
• If an angle is in degrees - multiply by π/180.

Sometimes you may encounter a problem where two or even three side lengths are missing. In such cases, the right triangle calculator, hypotenuse calculator and method on how to find the area of a right triangle won't help. You have to use trigonometric functions to solve for these missing pieces. This can be accomplished by hand or by using the triangle calculator.

The right triangle is just one of the many special triangles that exist. These triangles have one or several special characteristics that make them unique. For example, as we have seen, the right triangle has a right angle, and hence a hypotenuse, that makes it a unique kind of triangle. Aside from the right-angled triangle, there are other special triangles with interesting properties.

One of the most known special triangles is the equilateral triangle, which has three equal sides and all its angles are 60°. This makes it much more simple to make a triangle solver calculator, such as the equilateral triangle calculator, in which one can calculate different parameters of such a triangle.

Another of special triangles is the isosceles triangle, which has 2 sides of equal length, and hence two angles of the same size. As opposed to the equilateral triangle, isosceles triangles come in many different shapes, but all have certain properties that are exploited by the isosceles triangle calculator to obtain all the parameters of these triangles.

There are many other special triangles. However, we will now take a look at a few very special right triangles that besides being right-angled triangles, they have other special properties that make them interesting.

Among all the special right triangles, probably the most special is the so-called "45 45 90" triangle. This is a right-angled triangle that is also an isosceles triangle. Both its catheti are of the same length (isosceles) and it also has the peculiarity that the non-right angles are exactly half the size of the right angle that gives the name to the right triangle.

This right triangle is the kind of triangle that you can obtain when you divide a square by its diagonal. That is why both catheti (sides of the square) are of equal length. For those interested in knowing more about the most special of the special right triangles, we recommend checking out the 45 45 90 triangle calculator made for this purpose.

Another very interesting triangle from the group of special right triangles is the so-called "30 60 90" triangle. The name comes from having one right angle (90°), then one angle of 30° and another of 60°. These angles are special because of the values of their trigonometric functions (cosine, sine, tangent, etc.). The consequences of this can be seen and understood with the 30 60 90 triangle calculator, but for those who are too lazy to click the link, we will summarize some of them here. Assuming that the shorter side is of length a, the triangle follows:

1. the second length is equal to a√3,
2. the hypotenuse is 2a,
3. the area is equal to a²√(3/2),
4. the perimeter equals a(3 + √3).

It might seem at first glance that a right triangle and a parallelogram do not have anything in common. How can a triangle solver help you with understanding a parallelogram? The reality is that any parallelogram can be decomposed into 2 or more right triangles. Let's take an example of the rectangle which is the easiest one to see it.

Imagine a rectangle, any rectangle. Now draw trace on one of the diagonals of this rectangle (you can learn more about this in the diagonal of a rectangle calculator). If we separate the rectangle by the diagonal, what will we obtain is two right-angled triangles. Looking at the triangles, there is no need to use the right triangle calculator to see that both are equal, so their areas will be the same. This means that the area of the rectangle is double that of each triangle.

If we think about the equations, it makes sense since the area of a rectangle of sides a and b is exactly area = a * b, while for the right triangle is area = base * height / 2 which, in this case, would mean area = a * b /2. This is exactly what we already saw by just cutting the rectangle by the diagonal.

It was a simple example of a rectangle, but the same applies to the area of a square. For other parallelograms, the process becomes a bit more complicated (it might involve up to 4 right triangles of different sizes), but with a bit of skill, you can use the same idea and calculate the area of a parallelogram using right-angled triangles. You can, of course, be even more efficient and just use our calculator.

Geometry and polygons, especially triangles, always come together. The properties of some triangles, like right triangles, are usually interesting and shocking, even for non-mathematicians. We will now have a look at an interesting set of numbers very closely related to right-angled triangles that mathematicians love, and maybe you will too.

These sets of numbers are called the Pythagorean triplets and are sets of 3 integers (let's call the a, b and c) and satisfy the Pythagorean theorem: a² + b² = c². That is, they could form a right triangle with sides of length a, b and c. The amount of numbers that satisfy this relationship is limited but mathematicians find joy in searching for new ones.

Aside from the curiosity factor of this relationship, it has some interesting properties that are exploited in cryptography. Given the applications that one might find for such sets of numbers, mathematicians have explored even beyond, using 4, 5... and more sets of numbers that satisfy a similar relation in which the sum of the squares of all the numbers except for one, give the square of the number that's left.

Also very connected to these Pythagorean triplets is the infamous Fermat's last theorem in which the almost legendary cryptic mathematician Pierre Fermat stated that there could not be a set of three integer numbers that would satisfy the relation: aⁿ + bⁿ = cⁿ for n bigger than 2. This conjecture has not been proven mathematically and it's considered one of the most important mathematical problems of the century.

We have talked a lot about triangles, in particular, right triangles and their applications in maths and geometry. What we haven't talked about yet is the usefulness of right triangles for calculating things in real life. It might seem like the applications outside of geometry are limited, but let's have a look at shadows.

Yes, shadows. The dark shade projected by an object when it is illuminated. If you were to look at the shape made by the shadow, the object, and the ground, you would notice that it, in fact, a right-angled triangle! At least it is when the object is perfectly vertical, and the ground is horizontal. Most of the time this is the case or at least close enough. This means that we can use the right triangle calculator to find different pieces of information about objects under the sun. Let's see how.

Imagine that you have a building of which we want to know the height, but you cannot measure it directly because it's too high to drop a measuring tape from the top. What you can do is measure the length of the shadow on the street. Then, with the help of any angle-measuring tool and a piece of paper you can find out the angle between the shadow and the ground. Knowing that the angle between the building and the ground is 90°, you can input these data values into the right triangle side and angle calculator and obtain the value of the height of the building.

Using this technique, you can measure the height of many objects as long as you have a bright sunny day or other sources of light to illuminate the object. In fact, this use to be a very common measuring technique in the olden days. Probably the most interesting and mind-blowing use of right triangles is that of Eratosthenes, who managed to use right-angled triangles and shadows to measure the radius of the Earth, and now we are gonna explain how he did it.

Eratosthenes noticed that on the summer solstice there was a place on Earth where the wells did not have a shadow at midday, i.e., the sun shone straight down onto them. Noting this, he set up a column of a known height at a known distance from that well and measured the size of the shadow at the same time of the day and the same day of the year in both places. Then using right-angled triangles and trigonometry, he was able to measure the angle between the two cities and also the radius of the Earth, since he knew the distance between the cities.

It was quite an astonishing feat, that now you can do much more easily, by just using the Omni calculators that we have created for you.

Side lengths a, b, c form a right triangle if, and only if, they satisfy a² + b² = c². We say these numbers form a Pythagorean triple.

We have 4² =16 and 2² + 3² = 4 + 9 = 13, so the sum of squares of the two smaller numbers is NOT equal to the square of the largest number. That is, 2 3 and 4 does not form a Pythagorean triple, or, in other words, there is no right triangle with sides 2, 3, and 4.

For a right-angled triangle, the circumcenter, i.e., the center of the circle circumscribed on the triangle, coincides with the midpoint of the triangle's longest side (its hypotenuse).

The orthocenter of a right-angled triangle, i.e., the point where the triangle's altitudes intersect, coincides with the triangle's vertex of the right angle.