Question

A life guard in a tower 20 ft above sea level spots a struggling surfer at an angle of depression of 15 . How far is the surfer from the base of the tower?

Answer 1

Answer: $19.31\ ft$

Step-by-step explanation:

Given

The tower is at a height of $h=20\ ft$

the angle of depression is $15^{\circ}$

Suppose the surfer is x ft away from the base of the tower

$\therefore \text{From the figure, we can write}\\\\\Rightarrow \cos 15^{\circ}=\dfrac{x}{h}\\\\\Rightarrow x=h\cos 15^{\circ}\\\Rightarrow x=20\cos 15^{\circ}\\\Rightarrow x=19.31\ ft$

Therefore, the surfer is at a distance of 19.31 ft from the base of the tower.