A tree is leaning at a 5° angle from vertical, making an 85° angle with the ground. When the sun is at a 65° angle of elevation, the tree casts a 25-foot shadow. What is the approximate length of the tree?

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Mathematics

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9 October, 02:59

A tree is leaning at a 5° angle from vertical, making an 85° angle with the ground. When the sun is at a 65° angle of elevation, the tree casts a 25-foot shadow. What is the approximate length of the tree?

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Jazz · Answer 1

D = 25 ft is the length of a shadow. L - the length of a tree.

Two angles are 85° and 65° and the third is 180° - (65° + 85°) =

= 180° - 150° = 30°.

We will use the Sine Law:

25 / sin 30° = L / sin 65°

25 / 0.5 = L / 0.9063

25 * 0.9063 = 0.5 L

22.6577 = 0.5 L

L = 22.6577 : 0.5

L = 45.3 ft.

Answer: the approximate length of the tree is 45.3 ft.