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 = 120 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is θ = 29.0°. How wide is the river?

Answer 1

The river is 216.4851 m wide.

Explanation:

Take a look at the picture below, we observe that we have a triangle with a 90º angle and a 29º one, therefore, the third angle of the triangle would be

180 - 90 - 29 = 61º

We apply law of sines with this triangle to solve for x, where x is the width of the river

`(120)/(sin29) =(x)/(sin61)`

`x=120(sin61)/(sin29)\\x=120(.8746)/(.4848)\\x=216.4851`