Find x the angle of depression from the top of a lighthouse that is 181 ft above water level to the waterline of a ship 867 ft offshore. Round your answer to the nearest tenth of a degre
Draw a diagram.
Review your basic trig functions.
It should be clear that
tan x = 181/867
To find the angle of depression, you can use trigonometry, specifically the tangent function. The tangent of an angle can be calculated by dividing the length of the side opposite the angle by the length of the adjacent side.
In this case, the height of the lighthouse (181 ft) is the opposite side, and the distance from the lighthouse to the ship (867 ft) is the adjacent side.
So the tangent of the angle of depression (x) is given by:
tan(x) = opposite/adjacent
tan(x) = 181/867
To find the value of x, you need to take the inverse tangent (arctan) of both sides of the equation:
x = arctan(181/867)
Using a scientific calculator or online tools, you can find that arctan(181/867) is approximately 11.2 degrees.
Therefore, the angle of depression (x) from the top of the lighthouse to the waterline of the ship is approximately 11.2 degrees.