Question

Someone please help me with this question. I've been stuck on it for almost 40 minutes. Here's the question. Lauren was standing on the lifeguard stand on the beach trying to find her sister. She spotted her at the water's edge at an angle of depression of 12 degrees. If the stand is 5 yards above the sand, how far down the beach is Lauren's sister? Round your answer to the nearest yard.

Answer 1

24 yd

Explanation:

Treat x as the desired quantity. This x is the side of the triangle adjacent to the lower 12 degree angle. The side opposite this angle is 5 yds. Using the definition of the tangent,

tan 12 degrees = opp / adj = 5 yds / x

Then x = (5 yds) / (tan 12 degrees), or x = (5 yds) / 0.213

Then x = 24 yds (to the nearest yd)