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?
(2 points)
x = 61.04 feet and y = 35.01 feet
x = 35.01 feet and y = 61.04 feet
x = 35.01 feet and y = 35.70 feet
x = 71.41 feet and y = 87.17 feet

Answer 1

To solve for the height of the flagpole \( x \) and the distance \( y \) from Deshaun to the top of the flagpole, we can use the properties of right triangles and trigonometric functions.

1. **Finding Height of the Flagpole \( x \)**:
- Deshaun is 50 feet away from the base of the flagpole.
- The angle of elevation is 35 degrees.
- We can use the tangent function to find the height of the flagpole:

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

Where:
- \( \theta = 35^\circ \)
- Opposite side = height of the flagpole \( x \)
- Adjacent side = distance from Deshaun to the flagpole = 50 feet

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

Rearranging to solve for \( x \):

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

Using a calculator,

\[
\tan(35^\circ) \approx 0.7002
\]

Therefore,

\[
x = 50 \times 0.7002 \approx 35.01 \text{ feet}
\]

2. **Finding Distance \( y \)**:
- We can find the hypotenuse \( y \) using the cosine function:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Where:
- Adjacent side = 50 feet
- Hypotenuse side = distance to the top of the flagpole \( y \)

Rearranging:

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

Using a calculator,

\[
\cos(35^\circ) \approx 0.8192
\]

Therefore,

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

Putting it all together:

- Height of the flagpole \( x \approx 35.01 \) feet.
- Distance to the top of the flagpole \( y \approx 61.04 \) feet.

Thus, the correct answer is:

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