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 relevant trigonometric relationship

We know that in a right - triangle formed by the slope, the height (opposite side) and the base (adjacent side) with the given angle of the slope, if the length of the slope (hypotenuse) is $l = 50$ meters and the angle of the slope is $\theta=10^{\circ}$, and we want to find the height $h$ (opposite side to the angle $\theta$). We use the sine function $\sin\theta=\frac{opposite}{hypotenuse}$.

Step2: Substitute the values into the formula

We have $\sin\theta=\sin(10^{\circ})$ and $hypotenuse = 50$ meters. So $h = l\times\sin\theta$. Since $\sin(10^{\circ})\approx0.1736$, then $h = 50\times0.1736$.

Step3: Calculate the height

$h=50\times0.1736 = 8.68$ meters.

Answer:

The hiker will get approximately 8.68 meters high.