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 triangle type

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

Step2: Use sine in right triangle

In right triangle, $\sin(\frac{\theta}{2}) = \frac{2000}{2400}=\frac{5}{6}$.

Step3: Solve for $\frac{\theta}{2}$

$\frac{\theta}{2}=\arcsin(\frac{5}{6})$. Calculate $\arcsin(\frac{5}{6})\approx56.44^\circ$.

Step4: Find $\theta$

$\theta = 2\times56.44^\circ\approx112.9^\circ$.

Answer:

$112.9^\circ$