Question

1. two water slides are 50 meters apart on level ground. from the top of the taller slide, you can see the top of the shorter slide at an angle of depression of 15°. if you know that the top of the other slide is approximately 15 meters above the ground, about how far above the ground are you? round to the nearest tenth of a meter.

Explanation:

Step1: Define the height difference

Let the height of the taller slide be \( x \) meters. The height difference between the two slides is \( x - 15 \) meters. The horizontal distance between them is 50 meters, and the angle of depression is \( 15^\circ \), which is equal to the angle of elevation from the shorter slide to the taller slide.

Step2: Use tangent function

We know that \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). Here, \( \theta = 15^\circ \), opposite side is \( x - 15 \), and adjacent side is 50. So, \( \tan(15^\circ)=\frac{x - 15}{50} \).

Step3: Solve for \( x - 15 \)

First, find \( \tan(15^\circ) \approx 0.2679 \). Then, \( x - 15 = 50\times\tan(15^\circ) \approx 50\times0.2679 = 13.395 \).

Step4: Solve for \( x \)

Add 15 to both sides: \( x = 15 + 13.395 = 28.395 \approx 28.4 \).

Answer:

\( 28.4 \) meters