10.2 Solving Problems Involving Angle of Elevation and Angle of Depression

Posted on April 23, 2020 by user

Example:

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

Solution:

Step 1: 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.

$\begin{array}{l} \tan 52^{o} = \frac{10.9}{Q R} \\ Q R = \frac{10.9}{\tan 52^{o}} \\ Q R = 8.5 m \end{array}$

$\begin{array}{l} \tan {25.3}^{o} = \frac{10.9}{Q S} \\ Q S = \frac{10.9}{\tan {25.3}^{o}} \\ Q S = 23.1 m \end{array}$

QS – QR = (23.1 – 8.5) m = 14.6 m

Therefore the kid has cycled 14.6 metres.