To find the height of the flagpole, we will use some trigonometry.
Clyde's height from the ground is 6 feet, and he is looking up at the flagpole at an angle of elevation of 50 degrees. The distance from Clyde's face to the top of the pole is 25 feet.
Let's denote:
- \( h \) = height of the flagpole above Clyde's eye level,
- \( d \) = horizontal distance from Clyde to the base of the flagpole (which we will find),
- \( H \) = total height of the flagpole.
Since Clyde's eye level is 6 feet, the total height of the flagpole \( H \) is given by:
\[ H = h + 6 \]
From the given information, we know that:
- The distance from Clyde to the top of the pole (the hypotenuse) is 25 feet.
- The angle of elevation is 50 degrees.
Using the definition of the sine function in a right triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In our case, the opposite side is the height of the flagpole above Clyde's eye level \( h \) and the hypotenuse is 25 feet:
\[ \sin(50^\circ) = \frac{h}{25} \]
Solving for \( h \):
\[ h = 25 \cdot \sin(50^\circ) \]
Next, we can find \( \sin(50^\circ) \):
\[ \sin(50^\circ) \approx 0.7660 \]
So:
\[ h \approx 25 \cdot 0.7660 \approx 19.15 \text{ feet} \]
Now, we can find the total height of the flagpole \( H \):
\[ H = h + 6 \approx 19.15 + 6 \approx 25.15 \text{ feet} \]
Rounding to the nearest tenth, the height of the flagpole is:
\[ \boxed{25.2} \text{ feet} \]
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