Question

Find x, the angle of depression from the top of a lighthouse that is 199 ft above water level to the waterline of a ship 1104 ft off shore. Round your answer to the nearest tenth of a degree.

Answer 1

10.2°

Explanation:

I'm not sure if my answer is correct and I'm not too good at explaining but I'll try.

The height of the triangle would be 199 ft and it's length would be 1104 ft. Since were looking for the angle of depression, the angle would obviously be outside of our triangle (as shown in the picture). The height and length wouldn't change at all so we can just label the imaginary lines with their corresponding measurements.

The angle that we're looking for is marked in the picture. Since we are given the opposite and the adjacent side, we can use the inverse of tan to figure out our angle, which is 10.2°.

You can also use the "Z" rule and our angle would be where it's shown in the third picture. Nothing would change because our opposite side would still be 199 ft and our adjacent side would still be 1104 ft.