A man finds the angle of elevation of the top of a tree 14m high to be 30 degrees. Calculate the distance of the man from the foot of the tree.
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We can use the tangent function to find the distance of the man from the foot of the tree.
Let x be the distance of the man from the foot of the tree.
According to the given information, the height of the tree is 14m and the angle of elevation is 30 degrees.
Therefore, we have tan(30 degrees) = height / distance
tan(30 degrees) = 14 / x
To find x, we can rearrange the equation as follows:
x = 14 / tan(30 degrees)
x = 14 / 0.5774
x ≈ 24.21
Therefore, the man is approximately 24.21m away from the foot of the tree.