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`

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)=(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.