10.2 Solving Problems Involving Angles of Elevation and Depression

The angle of depression of a cycling kid measured from a hill with 10.9 m high is 52o. When the kid cycles along the hillside and stops, the angle of depression becomes 25.3o. What is the distance cycled by the kid along the hillside?

Step1: Draw a diagram to represent the situation.
Step 2: Devise a plan.
    Find the lengths of QS and QR. Then, QS – QR = distance cycled by the kid.

tan 52 o = 10.9 QR QR= 10.9 tan 52 o QR=8.5m

tan 25.3 o = 10.9 QS QS= 10.9 tan 25.3 o QS=23.1m

QS – QR = (23.1 – 8.5) m = 14.6 m

Therefore the kid has cycled 14.6 metres.