Question

1. demarius is at the bottom of a hill. the hill has an upward slope of 13.5° above horizontal. when demarius has walked 955 meters along this slope, how much elevation has he gained? 955 m 223 m 929 m 255 m

Explanation:

Step1: Recall the sine function in a right - triangle

In a right - triangle formed by the slope (hypotenuse \(c = 955\) m), the horizontal distance, and the elevation (opposite side to the angle \(\theta=13.5^{\circ}\)). The formula for the sine of an angle is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Let \(h\) be the elevation. So, \(\sin\theta=\frac{h}{c}\).

Step2: Solve for \(h\)

We know that \(c = 955\) m and \(\theta = 13.5^{\circ}\). Then \(h=c\times\sin\theta\). Substitute the values: \(h = 955\times\sin(13.5^{\circ})\). Since \(\sin(13.5^{\circ})\approx0.233\), then \(h=955\times0.233\).

$$h = 955\times0.233=(900 + 55)\times0.233=900\times0.233+55\times0.233=209.7+12.815 = 222.515\approx223$$

Answer:

223 m