Find x, the angle of depression (measured in degrees) from the top of a lighthouse that is 173 ft above water level to the waterline of a ship 4835 ft off shore. Round your answer to the nearest hundredth of a degree.
173/4835=0.03578076525336091
arctan(0.03578076525336091=2.049212625°
tan(tetha)=173/4835=0.002688728
tetha=arctan(0.002688728)=0,1540524°
tetha=0.15°
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle between the horizontal line of sight and the line of sight to the object being observed (in this case, the waterline of the ship).
In this scenario, we have a right triangle formed by the lighthouse, the ship, and the waterline. The height of the lighthouse (opposite side) is 173 ft and the distance from the lighthouse to the ship (adjacent side) is 4835 ft.
Using the trigonometric function tangent, we can calculate the angle of depression:
tan(theta) = opposite/adjacent
Let's substitute the values into the equation:
tan(theta) = 173/4835
Now, solve for theta by taking the inverse tangent of both sides:
theta = arctan(173/4835)
Using a calculator, we get:
theta ≈ 2.01 degrees
Therefore, the angle of depression from the top of the lighthouse to the waterline of the ship is approximately 2.01 degrees.