Question

Two planes just recently left the airport. Looking at the radar, Plane 1 is 50 miles away from the airport and Plane 2 is 200 miles away from the airport. If the 2 planes are 175 miles away from each other, what is the angle measurement from the airport to the 2 planes? (round to the nearest whole number)

Answer 1

To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:

Then;

`c^2=a^2+b^2-2ab\cos(C)`

Since we want to find the measure of angle x, we can use:

c = 175 mi

a = 200 mi

b = 50 mi

C = x

Now, by the Law of Cosines:

`175^2=200^2+50^2-2\cdot200\cdot50\cdot\cos(x)`

And solve:

`30625=40000+2500-20000\cos(x)`
`30625-40000-2500=-20000\cos(x)`
`(-11875)/(-20000)=\cos(x)`
`\begin{gathered} x=\cos^(-1)(0.59375) \\ . \\ x\approx53.5764 \end{gathered}`

To the nearest whole number, x = 54°