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,

Question

lukranit [14]

3 years ago

10

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?

Mathematics

1 answer:

Vinvika [58] · Answer 1 · 2022-03-06T10:04:04+03:00

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.