Question

1. a local hiker climbs a 50 - meter slope with a 10° gradient. a. create a drawing that displays the slope, vector components, and angle. b. how high will the hiker get?

Explanation:

Step1: Identify the trigonometric relation

We know that in a right - triangle formed by the slope, the height (opposite side) $h$, the length of the slope (hypotenuse) $d = 50$m and the angle of the slope $\theta=10^{\circ}$. The relation is $\sin\theta=\frac{h}{d}$.

Step2: Solve for the height

We can re - arrange the formula to $h = d\times\sin\theta$. Substitute $d = 50$m and $\theta = 10^{\circ}$ into the formula. Since $\sin(10^{\circ})\approx0.1736$, then $h=50\times0.1736 = 8.68$m.

Answer:

The hiker will get approximately 8.68 meters high.