Question

Choose the best answer. A 50-foot tree casts a shadow 75 feet long. The sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately _____.

Answer 1

Answer: 0.55

Explanation:

According to the trigonometry, in a right triangle :

`\sin\theta=\frac{\text{Side opposite to }\theta}{\text{Hypotenuse}}`

Given : A 50-foot tree casts a shadow 75 feet long.

Here , Side opposite to
`\theta` = 50 feet

In right triangle formed by tree , Let the hypotenuse be h.

According to the Pythagoras theorem, we have

`h^2=(50)^2+(75)^2\\\\ h^2=2500+5625=8125\\\\ h=√(8125)=90.1387818866\approx90.14`

Then,

`\sin\theta=(50)/(90.14)=0.554692700244\approx0.55`

Hence, the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately 0.55.

Answer 2

We use tan ratio to solve this problem. Look into my attachment for better understanding.

tan x = the side in front of the angle/ the side adjacent to the angle
tan x = 50/75
tan x = 2/3
x = tan⁻¹(2/3)
x = 33,69

x is approximately 34°