To determine the height of the movie screen, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is equal to the opposite side (height of the screen, \( h \)) over the adjacent side (distance from Kate to the base of the screen, \( d \)).
We have the following information:
- The angle of elevation, \( \theta = 24^\circ \)
- The distance from Kate to the base of the screen, \( d = 36 \) feet
The relationship can be expressed as: \[ \tan(\theta) = \frac{h}{d} \] Substituting the known values: \[ \tan(24^\circ) = \frac{h}{36} \]
Next, we can solve for \( h \): \[ h = 36 \cdot \tan(24^\circ) \]
Now, we will calculate \( \tan(24^\circ) \) and then find \( h \).
Using a calculator: \[ \tan(24^\circ) \approx 0.4452 \] Now substitute this value back into the equation for \( h \): \[ h = 36 \cdot 0.4452 \approx 16.0312 \]
Rounding to the nearest whole number, the height of the movie screen is approximately: \[ \boxed{16} \text{ feet} \]