Solve Applied Problems Using the Law of Cosines
-Two airplanes leave an airport at the same time, one going northwest (bearing $135 ^ { \circ }$ ) at $422 \mathrm { mph }$ and the other going east at $347 \mathrm { mph }$. How far apart are the planes after 2 hours (to the nearest mile)?
A) 1422 miles
B) 711 miles
C) 1184 miles
D) 1268 miles

Question

Quizplus · Accepted Answer

To solve this problem, we can use the Law of Cosines. First, we need to find the distance each plane has traveled after 2 hours. For the first plane going northwest at 422 mph, the distance traveled is $422 \times 2 = 844$ miles. For the second plane going east at 347 mph, the distance traveled is $347 \times 2 = 694$ miles. The angle between their paths is $135^\circ - 90^\circ = 45^\circ$ because the first plane's bearing is $135^\circ$ (northwest) and the second plane is going directly east ($90^\circ$ from north). Using the Law of Cosines: $d = \sqrt{844^2 + 694^2 - 2(844)(694)\cos(45^\circ)}$, which calculates to approximately 1422 miles.

Solve Applied Problems Using the Law of Cosines -Two Airplanes 135∘135 ^ { \circ }135∘

Solve Applied Problems Using the Law of Cosines
-Two Airplanes $135 ^ { \circ }$