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 101010 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^\circ40 ∘ 40, degrees. What is the width of the river? Round your final answer to the nearest hundredth. meters
Answers
Given : Trigonomos spotted a tree across the river and marked the spot directly across from it. Then he walked to another point 10 m down the river and found that the angle between his side of the river and the line connecting him to the tree was 40°C
To find : What is the width of the river
Solution:
Let say Tree is at point A
& Master Trigonomos is at point B
Then AB = Width of river
Trigonomos walked 10 m from B to C
BC = 10 m & ∠ABC = 90°
angle angle between his side of the river and the line connecting him to the tree was 40°C
∠BCA = 40°
ABC is a right angle Triangle
Tan ∠BCA = AB/BC
=> Tan 40° = AB/10
=> AB = 10 * Tan40°
=> AB = 10 * 0.839
=> AB = 8.39 m
Width of river = 8.39 m
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Answer:
it is either 60.16 or 8.39 m
Step-by-step explanation:
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