The angle of depression from the top of a tower 12m high at a point on the ground is 30

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

The angles of depression and elevation of the top of a 12m high building from the top and the bottom of a tower are 60° and 30° respectively. Find the height of the tower, and its distance from the building. 

Let AB be the building and CD be the tower. 

In ΔABD

`"AB"/"BD" = tan 30^circ`

`12/"BD" = 1/sqrt(3)`

`"BD" = 12sqrt(3)`

In ΔACE

`"AE" = "BD" = 12sqrt(3)`

`"CE"/"AE" = tan 60^circ`

`"CE"/(12sqrt(3)) = sqrt(3)`

`"CE" = 12sqrt(3) xx sqrt(3) = 12 xx 3 = 36`

`"CD" = "CE" + "ED" = 36 + 12 = 48`

So, height of the tower is 48 m and its distance from the building is `12sqrt(3)` m = `12 xx 1.732` m = 20.78 m(approximately)

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

  Is there an error in this question or solution?