**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:*

*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.

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

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

*QS – QR*= (23.1 – 8.5) m = 14.6 m

Therefore the kid has cycled

**14.6 metres**.