Question

5. Emily is standing on a bridge, looking down at a boat on the river. She knows that the bridge is 12m high, and estimates that the angle of depression between her and the boat is 55. How far is the boat from the base of the bridge, to the nearest tenth of a metre?

Answer 1

5. Emily is standing on a bridge, looking down at a boat on the river. She knows that the bridge is 12m high, and estimates that the angle of depression between her and the boat is 55°. How far is the boat from the base of the bridge, to the nearest tenth of a meter?

Angle of depression is the angle between a horizontal line and the line joining the observer's eye to some object beneath the horizontal line.

Let $x$ be the distance from the base of the bridge to the boat

Since the horizontal lines are parallel, the angles of elevation and depression are equal in measure.

$$\sin 55{}^{\circ} = \frac{12}{x}$$ $$x = \frac{12}{\sin 55{}^{\circ}}$$ $$x = 36,4 \, \text{m}$$

The distance from the base of the bridge to the boat is $36,4 \, \text{m}$.