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The angle of elevation measured from the ground at a spot 15 feet from the base of a tree is 63 degrees. How tall is the tree?

a) A = 13.4 ft
b) B = 29.4 ft
c) C = -6.8 ft
d) D = 32.1 ft

1 Answer

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Final answer:

To find the height of the tree, we use the tangent function with the angle of elevation and the distance from the tree. The calculation yields a height of approximately 29.4 feet, making the correct answer (b) 29.4 ft.

Step-by-step explanation:

The question involves finding the height of a tree given the distance from the tree and the angle of elevation. To solve this problem, we can use trigonometry, specifically the tangent function, which relates the opposite side (in this case, the height of the tree) to the adjacent side (the distance from the base of the tree).

The formula using the tangent of the angle is:

tan(\theta) = opposite/adjacent

Substituting the given values:

tan(63\degree) = height / 15 feet

Solving for the height gives us:

height = 15 feet * tan(63\degree)

height = 15 feet * 1.96261 (approximately)

height = 29.4 feet

Therefore, the correct answer is (b) 29.4 ft.

User Wachaga Mwaura
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