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.
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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 \( \tan(35^\circ) \):
\[ x \approx 50 \cdot 0.7002 \approx 35.01 \text{ ft} \]
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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.
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