Question

Two planes, A and B, start from the same place and move in different directions, making an angle of 50º between them. The speed of plane A is 200 miles per hour, and the speed of plane B is 300 miles per hour. The two planes are how many miles apart after one hour?

Answer 1

Answer: The distance between them is 230.65 miles.

Explanation:

Since we have given that

Speed of plane A (b) = 200 miles per hour

Speed of plane B (c) = 300 miles per hour

Angle between them = 50°

So,

We will use the "Cosine formula", we get

`a^2=b^2+c^2-2bc\cos A\\\\a^2=200^2+300^2-2* 200* 300\cos 50\textdegree\\\\a^2=40000+90000-120000\cos 50\textdegree\\\\a^2=130000-120000* 0.64\\\\a^2=130000-76800\\\\a^2=53200\\\\a=√(53200)\\\\a=230.65\ miles\ per\ hour`

So, distance between the two planes after one hour will be

`Distance=(Speed)/(time)=(230.65)/(1)=230.65\ miles`

So, the distance between them is 230.65 miles.