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 10 meters down the river and found that the angle between his side of the river and the line
connecting him to the tree was 40°.
What is the width of the river?
Round your final answer to the nearest hundredth.
meters

Answer 1

8.39

Explanation:

The width of the river is about 8.39 meters.

Answer 2

8.39 meters

Explanation:

The angle is opposite the side of interest of the right triangle representing the geometry. The adjacent side is known, so the tangent function can be useful.

Tan = Opposite/Adjacent

tan(40°) = width/(10 m) . . . . . filling in given values

(10 m)·tan(40°) = width ≈ 8.390996 m ≈ 8.39 m

The width of the river is about 8.39 meters.