To find the distance along the ground between Nisha's apartment building and the bottom of the sculpture, we can use the tangent function in trigonometry.
Given:
- The height of Nisha's window above the ground: \( h = 90 \) feet
- The angle of depression to the bottom of the sculpture: \( \theta = 22^\circ \)
The angle of depression is equal to the angle of elevation from the bottom of the sculpture to the top of the window.
We can set up the relationship with the tangent function: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] In this case:
- The opposite side is the height of Nisha's window which is \( 90 \) feet.
- The adjacent side is the distance along the ground, which we will call \( d \).
Thus, we have: \[ \tan(22^\circ) = \frac{90}{d} \]
To find \( d \), we can rearrange the equation: \[ d = \frac{90}{\tan(22^\circ)} \]
Now, we can calculate \( \tan(22^\circ) \): \[ \tan(22^\circ) \approx 0.4040 \]
Now substituting this value back into the equation for \( d \): \[ d \approx \frac{90}{0.4040} \approx 222.76 \text{ feet} \]
Thus, the distance along the ground between the building and the sculpture is: \[ \boxed{222.76 \text{ feet}} \]
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