SOLUTION: Two friends say ‘goodbye’ as they leave the school heading home in different directions. Jayshan walks 180 metres in one direction and Aneesa runs an unknown number of metres

Question 1190010: Two friends say ‘goodbye’ as they leave the school heading home in different directions. Jayshan
walks 180 metres in one direction and Aneesa runs an unknown number of metres in another direction
such that the angle between the friends is 72°. If the distance between the two friends is 485 metres,
then calculate how far Aneesa ran, rounding your answer to the nearest metre.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = how far Aneesa ran, in meters

Drawing is not to scale

Use the law of cosines to solve for x.
c^2 = a^2+b^2 - 2*a*b*cos(C)
485^2 = 180^2+x^2 - 2*180*x*cos(72)
485^2 = 180^2+x^2 - 2*180*x*0.30901699437494
235225 = 32400+x^2 - 111.246117974979x
0 = 32400+x^2 - 111.246117974979x - 235225
x^2 - 111.246117974979x - 202825 = 0

From here, you'll need the quadratic formula. I'll skip those steps but you should get the following roots:
x = -398.16
x = 509.41
both of which are approximate

We ignore the negative root. It doesn't make sense to have Aneesa run a negative distance.

The only practical solution here is roughly x = 509.41
This rounds to 509

Answer: 509 meters

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