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Sagot :
Answer:
Step-by-step explanation:
To find the length of the zip line, we can use trigonometry, specifically the tangent function, since we have the angle of depression and the horizontal distance:
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:
\[ L \approx 91 \cdot \tan(39^\circ) \]
\[ L \approx 91 \cdot 0.809784 \] (rounded to the nearest 100th)
\[ L \approx 73.79 \]
Therefore, the length of the zip line, rounded to the nearest hundredth, is \( \boxed{73.79} \) feet.
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