Question

at the park, a slide is 8 feet high and the base of the ladder forms a right angle with the ground. if the distance from the base of the ladder to the bottom of the slide is 8 feet, what is the angle of the slide with the ground, in degrees?

Explanation:

Step1: Identify the triangle type

The slide, ground, and ladder form a right - triangle. The height of the slide (opposite side to the angle we want to find) is 8 feet, and the base (adjacent side) is also 8 feet.

Step2: Use the tangent function

In a right - triangle, the tangent of an angle $\theta$ is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, opposite = 8 and adjacent = 8, so $\tan\theta=\frac{8}{8} = 1$.

Step3: Find the angle

We know that if $\tan\theta = 1$, then $\theta=\arctan(1)$. Since $\tan(45^{\circ}) = 1$, the angle $\theta = 45^{\circ}$.

Answer:

45