Question

1. an airplane is taking off from a runway. the airplane climbs from the runway at an angle of 18.5° above horizontal. when the airplane has flown 6.80 kilometers along the path, how much elevation has it gained?

6060 m
2160 m
6450 m
2290 m

Explanation:

Step1: Convert kilometers to meters

Since \(1\) kilometer \( = 1000\) meters, then \(6.80\) kilometers \(=6.80\times1000 = 6800\) meters.

Step2: Use the sine function

In a right - triangle (where the path of the airplane is the hypotenuse \(h = 6800\)m and the elevation \(y\) is the side opposite the angle \(\theta=18.5^{\circ}\)), the sine function is defined as \(\sin\theta=\frac{y}{h}\).
So, \(y = h\times\sin\theta\).
Substitute \(h = 6800\)m and \(\theta = 18.5^{\circ}\) (and \(\sin(18.5^{\circ})\approx0.317\)) into the formula:
\(y=6800\times\sin(18.5^{\circ})\approx6800\times0.317 = 2155.6\approx2160\)m.

Answer:

2160 m