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 1 5 1515 meters down the river and found that the angle between his side of the river and the line connecting him to the tree was 7 6 ∘ 76 ​∘ ​​ 76, degree. What is the width of the river? Round your final answer to the nearest hundredth.

Answer 1

width of the river is 60.16 m

Explanation:

Refer the attached figure

AB = width of river

We are required to find the width of river .

Since we are given that . Trigonomos spotted a tree across the river and marked the spot directly across from it.

Then he walked to the another point 15 meters down the river .i.e. BC = 15 m

He also found the angle between his side of the river and the line connecting him to the tree i.e. ∠ACB = 76°

So, now to calculate the width of river i.e. AB , we will use trigonometric ratio

`tan\theta = (Perpendicular)/(Base)`

`tan76^(\circ)= (AB)/(BC)`

`4.0107= (AB)/(15)`

`60.16=AB`

Thus the width of the river is 60.16 m