Question8. A surveyor in an airplane observes that the angle of depression to two points on the opposite shores of a lake are $32^{\circ}$ and $45^{\circ}$, respectively, as shown. What is the width of the lake, to the nearest metre, at those two points?

Studdy Solution
Now calculate the width of the lake $W$:
$$W = \frac{h}{\tan(32^\circ)} - h$$
$$W = \frac{3747.02}{0.6249} - 3747.02$$
$$W \approx 5995.12 - 3747.02$$
$$W \approx 2248.10$$
The width of the lake, to the nearest meter, is:
$$\boxed{2248}$$