A lighthouse operator is sending signals to a ship with a 17°
angle of depression. The height of the lighthouse is 40 feet relative to sea level. Which of the following correctly applies the sine ratio to find how far away the ship is from the top of the lighthouse? Round to the nearest tenth.
To find how far away the ship is from the top of the lighthouse, we can set up a right triangle with the height of the lighthouse (40 feet), the distance from the ship to the base of the lighthouse, and the angle of depression (17°).
Using the sine ratio, we have:
sin(17°) = opposite/hypotenuse
sin(17°) = 40 feet/hypotenuse
To find the hypotenuse (the distance from the ship to the top of the lighthouse), we can rearrange the equation:
hypotenuse = 40 feet / sin(17°)
hypotenuse ≈ 137.0 feet
Therefore, the ship is approximately 137.0 feet away from the top of the lighthouse.