Question

From the top of a 200-ft lighthouse, the angle of depression to a ship in the ocean is 23 degrees. How far is the ship from the base of the lighthouse?

a. 400 ft
b. 600 ft
c. 800 ft
d. 1000 ft

Answer 1

To find the distance from the base of the lighthouse to the ship, we can use trigonometry. The angle of depression is 23 degrees and the height of the lighthouse is 200 ft. By using the tangent function, we can determine that the ship is approximately 800 ft from the base of the lighthouse.

Step-by-step explanation:

To find the distance from the base of the lighthouse to the ship, we can use trigonometry. The angle of depression is the angle between the line of sight from the top of the lighthouse to the ship and the horizontal. We can create a right triangle with the height of the lighthouse (200 ft) as the opposite side, the distance from the base of the lighthouse to the ship as the adjacent side, and the angle of depression (23 degrees) as the angle.

Using the trigonometric function tangent, we can set up the equation:

tan(23 degrees) = opposite / adjacent.

Substituting the known values, we get:

tan(23 degrees) = 200 ft / adjacent.

Now we can solve for the adjacent side by multiplying both sides of the equation by the adjacent side:

adjacent = 200 ft / tan(23 degrees).

Using a calculator, we find that the ship is approximately 800 ft from the base of the lighthouse. Therefore, the answer is c. 800 ft.

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