Question

13.) an airplane at 2000 ft flies directly over a gun that has a range of 2400 ft as shown in the figure. what is the measure to the nearest tenth of a degree of the angle for which the airplane is within range of the gun?

Explanation:

Step1: Identify the triangle type

We have an isosceles triangle (two sides of 2400 ft, height 2000 ft). Split it into two right triangles, each with hypotenuse 2400 ft, opposite side 2000 ft.

Step2: Use sine for one right triangle

Let \(\theta/2\) be the angle in the right triangle. \(\sin(\theta/2)=\frac{2000}{2400}=\frac{5}{6}\)

Step3: Calculate \(\theta/2\)

\(\theta/2=\arcsin(\frac{5}{6})\approx\arcsin(0.8333)\approx56.44^\circ\)

Step4: Find \(\theta\)

\(\theta = 2\times56.44^\circ\approx112.9^\circ\)

Answer:

\(112.9^\circ\)