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 Q R Q R = 10.9 tan 52 o Q R = 8.5 m

tan 25.3 o = 10.9 Q S Q S = 10.9 tan 25.3 o Q S = 23.1 m

QS – QR = (23.1 – 8.5) m = 14.6 m

Therefore the kid has cycled 14.6 metres.

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