A $95 - \mathrm { t }$ tree casts a shadow that is$45$ Ft long. What is the angle of elevation of the sun?
A) $58.7 ^ { \circ }$
B) $25.3 ^ { \circ }$
C) $64.7 ^ { \circ }$
D) $47.3 ^ { \circ }$
E) $887 ^ { \circ }$

Question

Quizplus · Accepted Answer

Let's draw a diagram to help us visualize the problem:

```
           S
           /|
       95 / |
         /  | t
        /θ  |
       /    |
      /_____|              
         45
```

Here, S represents the position of the sun, and θ represents the angle of elevation we're trying to find. The tree is represented by a vertical line of length 95-t, and the shadow it casts is represented by a horizontal line of length 45.

Using the definition of the tangent function, we know that:

$$	an 	heta = \frac{	ext{opposite}}{	ext{adjacent}}$$

In this case, the opposite side is the height of the tree (95-t), and the adjacent side is the length of the shadow (45). So we have:

$$	an 	heta = \frac{95-t}{45}$$

To solve for θ, we can take the arctangent (or inverse tangent) of both sides:

$$	heta = \arctan \left( \frac{95-t}{45} ight)$$

Plugging this into a calculator, we get:

$$	heta \approx 64.7^\circ$$

Therefore, the answer is (C).

A 95−t95 - \mathrm { t }95−t Tree Casts a Shadow That Is

A $95 - \mathrm { t }$ Tree Casts a Shadow That Is