Submit th Suppose that you are headed toward a plateau 22.9 meters high. If the angle of elevation to the top of the plateau is \( 37.5^{\circ} \), how far are you from the base of the plateau? What is your distance from the base of the plateau? \( \square \) meters (Round to one decimal place as needed.)

To find the distance from the base of the plateau, you can use the tangent function from trigonometry, which relates the angle of elevation, the height of the plateau, and the distance to the base. The formula is: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] where \( \theta = 37.5^\circ \) and the opposite side is the height \( 22.9 \) meters. Rearranging the formula gives: \[ \text{adjacent} = \frac{\text{opposite}}{\tan(\theta)} = \frac{22.9}{\tan(37.5^\circ)} \] Calculating this, we first find \( \tan(37.5^\circ) \), which is approximately \( 0.7654 \). Thus, \[ \text{adjacent} = \frac{22.9}{0.7654} \approx 29.9 \text{ meters} \] So, the distance from the base of the plateau is approximately \( 29.9 \) meters.