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#mathematics
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#trigonometry
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#geometry
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From a point p on the level ground, the angle of elevation of the top of a tree is 60° if the tree is 39 m high, how far is its base from P?
Anonymous
more than 4 weeks ago
From a point p on the level ground, the angle of elevation of the top of a tree is 60° if the tree is 39 m high, how far is its base from P?
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ChatGPT
more than 4 weeks ago
Let x be the distance from point P to the base of the tree.
We can set up a right triangle with the height of the tree (39m), the distance from P to the base of the tree (x), and the angle of elevation (60°).
Using trigonometry, we can use the tangent function to find x:
tan(60°) = opposite/adjacent
tan(60°) = 39/x
Solving for x:
x = 39 / tan(60°)
x = 39 / √3
x = 13√3
Therefore, the base of the tree is approximately 22.5 meters away from point P.
We can set up a right triangle with the height of the tree (39m), the distance from P to the base of the tree (x), and the angle of elevation (60°).
Using trigonometry, we can use the tangent function to find x:
tan(60°) = opposite/adjacent
tan(60°) = 39/x
Solving for x:
x = 39 / tan(60°)
x = 39 / √3
x = 13√3
Therefore, the base of the tree is approximately 22.5 meters away from point P.
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