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Otrada [13]
3 years ago
7

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?
Mathematics
1 answer:
GalinKa [24]3 years ago
7 0

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.

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