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)
Responses

x=71.41 ft.and y=87.17 ft.
x equals 71.41 ft. and x equals 87.17 ft.

x=35.01 ft. and y=35.70 ft.
x equals 35.01 ft. and x equals 35.70 ft.

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

x=61.04 ft. and y=35.01 ft.

Answer 1

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

1. **Finding the height of the flagpole (x)**:
We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the height of the flagpole is the opposite side, and the distance to the flagpole is the adjacent side.

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where \( \theta \) is the angle of elevation, opposite is the height \( x \), and adjacent is the distance (50 feet).

\[
\tan(35^\circ) = \frac{x}{50}
\]

Solving for \( x \):

\[
x = 50 \cdot \tan(35^\circ)
\]

Using a calculator to find \( \tan(35^\circ) \):

\[
x \approx 50 \cdot 0.7002 \approx 35.01 \text{ ft}
\]

2. **Finding the distance to the top of the flagpole (y)**:
We can use the hypotenuse of the triangle, which can be found using the cosine function. The hypotenuse \( y \) is calculated as follows:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
where the adjacent side is 50 feet, and we want to find \( y \).

Rearranging gives:

\[
y = \frac{50}{\cos(35^\circ)}
\]

We know \( \cos(35^\circ) \approx 0.8192 \):

\[
y \approx \frac{50}{0.8192} \approx 61.04 \text{ ft}
\]

With these calculations, we find:

- The height of the flagpole \( x \approx 35.01 \text{ ft} \)
- The distance to the top of the flagpole \( y \approx 61.04 \text{ ft} \)

Thus, the correct response is:

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