Find the depth of a fishing hook to the nearest foot given t

Find the depth of a fishing hook, to the nearest foot, given the angle of depression alpha= 31.3323 degrees, that the 25 ft of fishing line makes with the surface of the water.

A) 13 ft

B) 21 ft

C) 15 ft

D) 5 ft

PLEASE SHOW WORK!

Solution

draw the diagram.

you have a right triangle, with one acute angle being alpha, and the hypotenuse being the 25 ft of fishing line.

the side opposite alpha is the depth of the fishing hook.

sine = opposite / hypotenuse

sin(31.3323)º = x / 25

x = 25*sin(31.3323)º 13 feet