Answer:
C. 5126 feet.
Step-by-step explanation:
To solve this problem, we have to apply the law of cosines.
According to the problem, the distance of the first plane to the radar tower is [tex]p_{1}= 2400ft[/tex] and the distance of the second plane to the radar tower is [tex]p_{2}=3200ft[/tex]. Additionally, the angle between these two distances is [tex]\theta = 132\°[/tex].
So, if we apply the law of cosine, we have
[tex]x^{2}=p_{1}^{2}+ p_{2}^{2}-2p_{1}p_{2}cos\theta[/tex]
Replacing all given values, we have
[tex]x^{2}=(2400)^{2}+ (3200)^{2}-2(2400)(3200)cos132\°\\x=\sqrt{16000000-15360000(-0.67)}\approx 5127.5ft[/tex]
Therefore, the right answer is C. 5126 feet.
(The difference between digits is due to the number of decimals we used in the operations)
