Question

A boat is spotted in the water with an angle of depression of 25° from the top of a lighthouse that is 89 feet tall. To the nearest foot, how far away is the boat from the base of the lighthouse?

A)
37 feet
B)
42 feet
C)
98 feet
D)
191 feet

Answer 1

Its basically asking for the base so "adjacent" would be "X" and the only place 89 can go is on the opposite so we have

tan(25) = 89/x
x*tan(25) =89
x=89/tan(25) and we get 191 :D

Make sure your calculator is in degree mode

Answer 2

To calculate this you need to imagine triangle which points are:
boat
Top of lighthouse
Bottom of lighthouse

That triangle has 90 degrees angle at bottom of lighthouse. That means that we can use trigonometry to determine length between boat and bottom of lighthouse

tan(25) = 89/x
x = 89/tan(25)
x = 190.86

after rounding, the answer is D, 191 feet