Everything Maths Grade 10

Worked example 4: Angles of elevation and depression

QUESTION

A block of flats is 200 m away from a cellphone tower. Someone stands atB. They measure the angle from
Bto the top of the tower (E) to be 34° (the angle of elevation). They then measure the angle fromBto the
bottom of the tower (C) to be 62° (the angle of depression).

What is the height of the cellphone tower (correct to the nearest metre)?

C

D

A

B

E

34 ◦

62 ◦

200 m

Note: diagram not drawn to scale

SOLUTION

Step 1: To determine heightCE, first calculate lengthsDEandCD

△BDEand△BDCare both right-angled triangles. In each of the triangles, the lengthBDis known. Therefore
we can calculate the sides of the triangles.

Step 2: CalculateCD

The lengthACis given.CABDis a rectangle soBD=AC=200 m.

In△CBD:

tanCBD^ =

CD

BD

)CD=BDtanCBD^

= 200tan 62 °

=376,1452...

376 m

Step 3: CalculateDE

In△DBE:

tanDBE^ =

DE

BD

)DE=BDtanDBE^

= 200tan 34 °

=134,9017...

135 m

Step 4: Add the two heights to get the final answer

The height of the tower is:CE=CD+DE=135 m+376 m=511 m.

Chapter 11. Trigonometry 395