Solve the problem.
-A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 130 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is $50 ^ { \circ }$. What is the distance between the piling and the pier to the nearest foot?
A) 155 feet
B) 100 feet
C) 84 feet
D) 109 feet

Question

Quizplus · Accepted Answer

The distance between the piling and the pier is the length of the opposite side of a right triangle with an angle of 50 degrees and an adjacent side of 130 feet. Using the tangent function, we can find the length of the opposite side: tan(50 degrees) = opposite/130 feet. Solving for the opposite side, we get opposite = 130 feet * tan(50 degrees) = 154.9 feet. Rounding to the nearest foot, the distance between the piling and the pier is 155 feet.

Solve the Problem 50∘50 ^ { \circ }50∘ What Is the Distance Between the Piling and the a Small

Solve the Problem $50 ^ { \circ }$ What Is the Distance Between the Piling and the a Small