Answer :

Final answer:

To solve this problem, we apply the tangent function (part of trigonometry), which we rearrange to find the length of the shadow. Substituting the given values, a 20m tall tree under the sun at an altitude of 62 degrees will cast a shadow of approximately 12.02m.

Explanation:

This question involves the application of trigonometry to calculate the length of a shadow. The altitude of the sun, in this case, is the angle formed between the line indicating the sun's position and a horizontal line from the tip of the tree to the horizon. The angle is given as 62 degrees. The shadow is simply the adjacent side of this angle.

To find this, we use the tangent function which is of the form tan(θ) = opposite side/adjacent side. Here, the opposite side is the height of the tree, which is 20m. So, we rearrange the formula to solve for the length of the shadow i.e. adjacent side = opposite side/tan(θ). Substituting the values we have, the length of the shadow = 20m/tan(62) = approx. 12.02m. Hence, if a 20m tall tree is under the sun at an altitude of 62 degrees, it will cast a shadow of approximately 12.02m.

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