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 2 years ago
To find the height of a tall tree, a surveyor moves 140 feet away from the base of the tree and then, with a transit 4 feet tall, measures the angle of elevation to the top of the tree to be 53°. What is the height of the tree?
 2 years ago
To find the height of a tall tree, a surveyor moves 140 feet away from the base of the tree and then, with a transit 4 feet tall, measures the angle of elevation to the top of the tree to be 53°. What is the height of the tree?

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mubzz
 2 years ago
Best ResponseYou've already chosen the best response.1In order to solve this question, you need to use trigonometry and the rules of similar triangles. To find 'y', we use trigonometry. \[\tan 37 = y \div 4\] y = 4 tan37 y = 3.014 Now you need to find 'x' and that will help you find the height of the tree Using similar triangles, we get the following relation: \[(140+y)/(x+4) = 140/x\] we know y to be 3.014 so this becomes \[(143.014)/(x+4) = 140/x\] Now you cross multiply and solve for 'x' 140(x+4) = 143.014(x) 3.014x = 560 x = 185.8 feet Height of tree according to figure = x+4 height of tree is approximately 190 feet
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