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.
Accepted Solution
A:
Answer:60.2 mStep-by-step explanation:Let x represent the width of the river. The distance from the point across from the tree to the second point is 15 m. The angle from this point to the tree across the river is 76°.This makes the side opposite the angle x, the width of the river. It also means the 15 m side is adjacent to this angle.The ratio opposite/adjacent is the ratio for tangent; this gives us the equationx/15 = tan(76)Multiply both sides by 15:15(x/15) = 15(tan(76))x = 15(tan(76)) ≈ 60.2