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.
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