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? Round to the nearest hundredth place (2 decimal places). C x feet < 8 of 17 Item 7 Itern 8 Item 9 Item 10 Item 11 Item 12 Item 13 Item 14 y feet A 350 50 feet B (2 points) feet and y feet.

Answer 1

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

1. **Finding the height of the flagpole (x):**

Using the tangent function, which relates the angle of elevation to the opposite side (the height of the flagpole) and the adjacent side (the distance from Deshaun to the flagpole):
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case:
- \(\theta = 35°\)
- The adjacent side = 50 feet
- The opposite side = x (height of the flagpole)

So we have:
\[
\tan(35°) = \frac{x}{50}
\]

To find x, we can rearrange the equation:
\[
x = 50 \cdot \tan(35°)
\]

Calculating:
\[
x = 50 \cdot \tan(35°) \approx 50 \cdot 0.7002 \approx 35.01 \text{ feet}
\]

2. **Finding the distance to the top of the flagpole (y):**

Now, we can use the hypotenuse of the right triangle formed by Deshaun, the base of the flagpole, and the top of the flagpole. We can use the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Thus:
\[
\sin(35°) = \frac{x}{y}
\]

From here, we can rearrange to find y:
\[
y = \frac{x}{\sin(35°)}
\]

Substituting in the value of x we just calculated:
\[
y = \frac{35.01}{\sin(35°)} \approx \frac{35.01}{0.5736} \approx 61.00 \text{ feet}
\]

Now, rounding both x and y to two decimal places:
- Height of the flagpole (x) = **35.01 feet**
- Distance to the top of the flagpole (y) = **61.00 feet**

**Final Answers:**
- Height of the flagpole (x): **35.01 feet**
- Distance to the top of the flagpole (y): **61.00 feet**