Question

A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 118 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is = 33.4°. How wide is the river?

Answer 1

68.5 meters

Step-by-step explanation:

To solve this problem, we can use trigonometry and create a right triangle with the river as the hypotenuse.

Let's call the width of the river "w". We can use the sine function to find the length of the opposite side of the triangle (the distance from the surveyor to the tree).

sin(33.4°) = opposite/hypotenuse

sin(33.4°) = w/x

w = x * sin(33.4°)

w = 118 m * sin(33.4°)

w = 68.5 m

Therefore, the width of the river is approximately 68.5 meters.