Question

The people of Bridgetown wanted to build a bridge across a nearby river. Since they were poor swimmers, their master Trigonomos agreed to measure the width of the river without actually crossing it. Trigonomos spotted a tree across the river and marked the spot directly across from it. Then he walked to another point 151515 meters down the river and found that the angle between his side of the river and the line connecting him to the tree was 76^\circ76 ∘ 76, degrees. What is the width of the river?

Answer 1

60.16 m

Explanation:

Let w = width of river

Using trigonometry :

The width, w of the river is can be calculated thus :

Tan θ = opposite / Adjacent

Tan 76 = w / 15

4.0107809 = w / 15

w = 15 * 4.0107809

w = 60.1617 m

Hence, width of the river is 60.16 m