What is the angle of elevation of the sun when a tree 7.5 m tall casts a shadow 10.1 m long ?
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tan(θ) = 7.5 / 10.1
To calculate the angle of elevation of the sun, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the height of the tree is the opposite side (the vertical distance from the ground to the top of the tree), and the length of the shadow is the adjacent side (the horizontal distance from the base of the tree to the tip of the shadow).
So, the formula we can use is:
tan(angle) = opposite/adjacent
Substituting the given values, we have:
tan(angle) = 7.5 m / 10.1 m
To find the angle, we take the inverse tangent (also known as arctan or atan) of both sides:
angle = arctan(7.5 m / 10.1 m)
Using a calculator or a trigonometric table, we can find the value of the inverse tangent of 7.5 divided by 10.1.
angle ≈ 38.2 degrees
Therefore, the angle of elevation of the sun is approximately 38.2 degrees.