Answer to Question #293857 in Trigonometry for Lei

Question

A surveyor is measuring a river’s width. He uses a tree and a big rock that are on the edge of 

the river on opposite sides. After turning through an angle of 90° at the big rock, he walks 100 

meters away to his tent. He finds the angle from his walking path to the tree on the opposite side 

to be 25°. What is the width of the river?

Answer 1

Explanation & Calculations

• It can be figured out that the distance from the rock to his tent is 100 meters.
• Then if you consider the tangent that could be applied to the virtual triangle which can be drawn linking the tree, the tent and the rock, you could see the following which leads to the answer,

$\qquad\qquad \begin{aligned} \small \tan 25^0&=\small \frac{\text{Length of the river}}{100\,m}\\ \small \text{Length of the river} &=\small 100\times\tan 25^0\\ &=\small 46.6\,m \end{aligned}$