To find the angle of depression from the top of the lighthouse to the water line of the ship, we can use trigonometry.
1. First, let's convert 2½ miles to feet. Since 1 mile is equal to 5280 feet, 2½ miles is 2.5 x 5280 = 13200 feet.
2. Next, we have a right triangle where the height of the lighthouse is 275 feet and the horizontal distance to the ship is 13200 feet.
3. The angle of depression is the angle formed by the line of sight from the top of the lighthouse to the water line of the ship and the horizontal line. This angle is the same as the angle of elevation for an observer on the ship looking up to the top of the lighthouse.
4. To find the angle of depression, we can use the tangent function. Tangent(theta) = opposite/adjacent. In this case, tan(theta) = 275/13200.
5. Now, we can find the angle by taking the arctangent of (275/13200) using a calculator. This will give us the angle of depression.
6. Make sure to use the units of measurement provided (feet and miles) consistently throughout the calculation to ensure accuracy.
By following these steps, you can determine the angle of depression from the top of the lighthouse to the water line of the ship accurately.
