The Exciting Calculation of Horizontal Distance to a Lighthouse

What is the horizontal distance from a ship to the base of a 200-foot-tall lighthouse given an angle of depression of 14°?

A) 50 feet

B) 194 feet

C) 206 feet

D) 802 feet

Answer:

The horizontal distance from a ship to the base of a 200-foot-tall lighthouse with an angle of depression of 14° is approximately 802 feet.

Understanding trigonometric principles can lead us to fascinating applications, such as calculating the horizontal distance from a ship to a lighthouse. In this scenario, with an angle of depression of 14°, we can apply the tangent function to determine the distance.

The angle of depression is equal to the angle of elevation, as both angles are congruent when a line is parallel to the ground. This relationship allows us to use the tangent function, which involves the ratio of the opposite side to the adjacent side in a right triangle.

By denoting the distance from the ship to the lighthouse as x, we can set up the equation tangent(14°) = 200/x to find the value of x. After calculations, we discover that the horizontal distance is approximately 802 feet, making option D) 802 feet the correct answer after rounding to the nearest foot.