Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree.
-A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 140 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 40°. What is the distance between the piling and the pier to the nearest foot?
A) 117 feet
B) 90 feet
C) 107 feet
D) 167 feet

Question

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree. 
-A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 140 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 40°. What is the distance between the piling and the pier to the nearest foot?
A) 117 feet 
B) 90 feet 
C) 107 feet 
D) 167 feet

Quizplus · Accepted Answer

The distance between the piling and the pier is the opposite side of a right triangle with an angle of 40° and an adjacent side of 140 feet. Using the tangent function, we can find the opposite side: tan(40°) = opposite/140, so opposite = 140 * tan(40°) ≈ 117 feet.

Solve the Right Triangle Shown in the Figure