We can solve this problem using trigonometry. Let's consider the triangle formed by the man, the tree, and the top of the building.
In this triangle, the angle of elevation of the top of the tree is 22° and the distance between the man and the building is 15m. The height of the building is given as 24m.
We can use the tangent function to find the height of the tree. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Let's call the height of the tree "h" since that's what we need to find.
From the given information, we can set up the following equation:
tan(22°) = h / 15
To solve for h, we multiply both sides of the equation by 15:
15 * tan(22°) = h
Using a calculator, we find that 15 * tan(22°) ≈ 5.62
So the height of the tree is approximately 5.62m.
Similarly, for the angle of elevation of 32°, we can set up the following equation:
tan(32°) = h / 15
To solve for h, we multiply both sides of the equation by 15:
15 * tan(32°) = h
Using a calculator, we find that 15 * tan(32°) ≈ 9.61
So the height of the tree is approximately 9.61m.
A man1.5m tall is 15m away from the building,24m high What is the angle of elevation of the top of the tree are 22° and 32° reprehensively. Find the height of the tree
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