Question

You are standing at the top of the Charleston Lighthouse. While looking out, you look down at an angle of depression of 27 degrees and see a boat. If the lighthouse is 140 feet tall, what is the horizontal distance between the boat and the bottom of the lighthouse?

Answer 1

Horizontal distance = 71.3ft

Step-by-step explanation:

Let x be the horizontal distance between the light house and the boat

The horizontal distance can be calculated by using SOH CAH TOA

The opposite side = x

The adjacent side = 140 ft

Tan 27 = opposite / adjacent

Tan 27 = x / 140

Cross multiply

x = tan 27 * 140

tan 27 = 0.5095

x = 0.5095 x 140

x = 71.3 ft

Therefore, the horizontal distance is 71.3ft