A surveyor wants to find the distance across a river. A stake is placed on each bank of the river as shown in the figure. She measures a distance of 30.0 m from one stake to another on the same side of the river, thus finding the third vertex on a right triangle. She then measures the angle $\theta$ and finds it equal to 75.9°. What is the distance across the river?
A)89.2 m
B)15.3 m
C)119 m
D)268 m
E)29.0 m

Question

A surveyor wants to find the distance across a river. A stake is placed on each bank of the river as shown in the figure. She measures a distance of 30.0 m from one stake to another on the same side of the river, thus finding the third vertex on a right triangle. She then measures the angle $\theta$ and finds it equal to 75.9°. What is the distance across the river? 
A)89.2 m 
B)15.3 m 
C)119 m 
D)268 m 
E)29.0 m

Quizplus · Accepted Answer

We can use trigonometry to solve this problem. Let x be the distance across the river. Then we can use the sine function to find x:

sin(75.9°) = x / 30.0

x = 30.0 * sin(75.9°) ≈ 29.0 m

Therefore, the distance across the river is approximately 29.0 m. The closest answer choice is C, so we choose it.

A Surveyor Wants to Find the Distance Across a River θ\thetaθ

A Surveyor Wants to Find the Distance Across a River $\theta$