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Ali stands 2.5 m away from a tree. When he looks at the top of the tree, the line of his sight makes an angle of 40° with the horizontal. Ali’s eye-level is 1.6 m from the ground. Find the height of the tree​

Ali stands 2.5 m away from a tree. When he looks at the top of the tree, the line-example-1
User Lee Gary
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If you draw out a diagram of the situation, the height of the person is 5.5 feet, standing 25 feet away from the tree. then the person looks up at a 71 degree angle with the top of the tree, it should look like a right triangle on top of a rectangle.

We know the angle she's looking at (71 degrees) and the side adjacent to the angle (the distance she is away from the tree, 25 feet). Using tangent we can solve for the opposite side.

tan(71 degrees) = x ÷ 25
25 tan (71 degrees) = x
x is about 72.6 feet

that's the height from her eyes to the top of the tree.
To get the height of the tree you add how high above the ground her eyes are (5.5 feet) to x (72.6 feet)

72.6 + 5.5 = 78.1 feet

that should be the height of the tree
User Borjovsky
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