The height of a tower is 15m. what is the length of its shadow when suns altitude is 45°

The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 15 seconds the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 

Let A be the point of observation, C and E be the two points of the plane. It is given that after 15 seconds angle of elevation changes from 60° to 30°.

[Since jet plane is flying at constant height, therefore, CB = ED = 

In right triangle ABC, we have

In right triangle ADE, we have

Putting the value of (i) in (ii), we get1500 + BD = 4500⇒    BD = 3000∵ Distance travelled in 15 sec=  CE = BD = 3000 metres,

Now, speed of plane (m/s)     =    

and speed of plane (km/h)     =   

The height of a tower is 10 m. What is the length of its shadow when Sun's altitude is 45°?

Let BC be the length of shadow is x m 

Given that: Height of tower is 10 meters and altitude of sun is 45°

Here we have to find length of shadow.

So we use trigonometric ratios. 

In a triangle ABC,

`⇒ tan = (AB)/(BC)`   

`⇒ tan 45°=(AB)/(AC)` 

`⇒1=10/x`

`⇒x=10`

Hence the length of shadow is 10 m.

Concept: Heights and Distances

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If the ratio of the height of a tower and the length of its shadow is `sqrt3:1`, what is the angle of elevation of the Sun?

Let C be the angle of elevation of sun is θ. 

Given that: Height of tower is `sqrt3` meters and length of shadow is 1.

Here we have to find angle of elevation of sun.

In a triangle ABC, 

`⇒ tanθ =(AB)/(BC)` 

`⇒ tan θ=sqrt3/1`        ` [∵ tan 60°=sqrt3]`

`⇒ tan θ=sqrt3`

`⇒ θ=60 °`

Hence the angle of elevation of sun is 60°.

Concept: Heights and Distances

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