Find $x$, the angle of depression from the top of a lighthouse that is $194 \mathrm{ft}$ above water level to the waterline of a ship $1011 \mathrm{ft}$ off shore. Round your answer to the nearest tenth of a degree.
Espantol
\[
x=\square \cdot
\]
Answer
So, the angle of depression from the top of the lighthouse to the waterline of the ship is \(\boxed{10.9}\) degrees.
Step 1 ：Given that the height of the lighthouse is 194 ft and the distance to the ship is 1011 ft, we can use the tangent of the angle of depression, which is the ratio of the opposite side to the adjacent side in a right triangle.
Step 2 ：In this case, the opposite side is the height of the lighthouse and the adjacent side is the distance to the ship.
Step 3 ：We can use the arctangent function to find the angle.
Step 4 ：After calculation, we find that the angle is approximately 10.9 degrees.
Step 5 ：So, the angle of depression from the top of the lighthouse to the waterline of the ship is \(\boxed{10.9}\) degrees.
