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Sagot :
Answer:
Explanation:
To find the length of the zip line correctly, let's revisit the problem with the correct conversion of the angle of depression.
Given:
- Angle of depression \( \theta = 39^\circ \)
- Horizontal distance \( x = 91 \) feet
Let \( L \) denote the length of the zip line.
The tangent of the angle of depression is defined as the ratio of the opposite side (height of the building) to the adjacent side (horizontal distance):
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{L}{x} \]
Substitute the given values:
\[ \tan(39^\circ) = \frac{L}{91} \]
Now, solve for \( L \):
\[ L = 91 \cdot \tan(39^\circ) \]
Using a calculator to find \( \tan(39^\circ) \):
\[ \tan(39^\circ) \approx 0.809784 \]
Now calculate \( L \):
\[ L \approx 91 \cdot 0.809784 \]
\[ L \approx 73.91 \]
Therefore, the length of the zip line, rounded to the nearest hundredth, is \( \boxed{73.91} \) feet. This is the correct length of the zip line considering the angle of depression and horizontal distance provided.
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