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21 votes
21 votes
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)

Two planes just recently left the airport. Looking at the radar, Plane 1 is 50 miles-example-1
User Favoretti
by
2.7k points

1 Answer

22 votes
22 votes

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°

Two planes just recently left the airport. Looking at the radar, Plane 1 is 50 miles-example-1
User Vijay C
by
3.0k points
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