Question

1. a ski slope has an angle of elevation of 23°. a which ratio would you use to determine the height of the ski slope? explain your choice.

Explanation:

Step1: Identify sides relative to angle

We have a right triangle: the given angle is $23^\circ$, the adjacent side to this angle is 3076 ft, and $x$ (the height) is the opposite side to the $23^\circ$ angle.

Step2: Select trigonometric ratio

The tangent function relates opposite and adjacent sides of a right triangle:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta = 23^\circ$, opposite side = $x$, adjacent side = 3076 ft. We use tangent because we know the adjacent side and need the opposite side (height).

Answer:

We use the tangent ratio, $\tan(23^\circ) = \frac{x}{3076}$. This is because tangent relates the opposite side (the unknown height $x$) and the adjacent side (the known 3076 ft length) to the given $23^\circ$ angle in the right triangle.