Question

Deshaun is looking up at a flag that is 50 feet away from him at an angle of elevation from ground level of
35° What is the flagpole's height, x, and the distance between Deshaun and the top of the flagpole, y? (1 point)
• x = 71.41 ft. and y = 87.17 ft.
• x = 35.01 ft. and y = 61.04 ft.
• x = 61.04 ft. and y = 35.01 ft.
• x = 35.01 ft. and y = 35.70 ft.

Answer 1

To find the height of the flagpole (x) and the distance from Deshaun to the top of the flagpole (y), we can use some trigonometry.

Given:
- Distance from Deshaun to the base of the flagpole = 50 feet
- Angle of elevation = 35°

### Step 1: Find the height of the flagpole (x)

We can use the tangent function, which relates the height of the flagpole to the distance from Deshaun:

\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case, the "opposite" side is the height of the flagpole (x) and the "adjacent" side is the distance from Deshaun to the base of the flagpole (50 ft):

\[
\tan(35°) = \frac{x}{50}
\]

To solve for x:

\[
x = 50 \cdot \tan(35°)
\]

Calculating \( \tan(35°) \):

\[
\tan(35°) \approx 0.699
\]

So,

\[
x \approx 50 \cdot 0.699 \approx 34.95 \text{ feet}
\]

### Step 2: Find the distance from Deshaun to the top of the flagpole (y)

To find this, we can use the sine function:

\[
\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Here, the hypotenuse is the distance from Deshaun to the top of the flagpole (y) and the opposite remains x.

Thus,

\[
\sin(35°) = \frac{x}{y}
\]

We can rearrange this to solve for y:

\[
y = \frac{x}{\sin(35°)}
\]

Calculating \( \sin(35°) \):

\[
\sin(35°) \approx 0.5736
\]

Substituting the value of x:

\[
y \approx \frac{34.95}{0.5736} \approx 61.00 \text{ feet}
\]

### Summary of Results

The calculations yield:
- Height of the flagpole \( x \approx 34.95 \text{ feet} \)
- Distance to the top of the flagpole \( y \approx 61.00 \text{ feet} \)

### Conclusion

The closest option that matches our calculations is:

**x = 35.01 ft. and y = 61.04 ft.**