SOLUTION: A triangle field ABC is such that AB=90 m, BC=70 m & AC=85 m. Make a scale drawing of it, using a scale of 1 cm to 10 m. From your scale drawing, find (a) the actual distance fro

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Question 1090577: A triangle field ABC is such that AB=90 m, BC=70 m & AC=85 m. Make a scale drawing of it, using a scale of 1 cm to 10 m. From your scale drawing, find
(a) the actual distance from A to the midpoint of BC and,
(b) the actual distance from B to the midpoint of AC.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Not sure how you get actual distances from a scale drawing.
You can get an estimate of the distances.
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I'm solving it algebraically.
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So let's set up a coordinate system with (0,0) at A.
So then B is (90,0).
Angle A is 47.1.
Angle B is 62.7.
Angle C is 70.2.
So then the coordinates of C is
C:(85cos%2847.1%29,85sin%2847.1%29)
C:(57.86,62.27)
The midpoint of AC would then be half of those values.
M%5BAC%5D=(28.9,31.2)
So then using the distance formula.
D%7B1%5D%5E2=%2890-28.9%29%5E2%2B%280-31.2%29%5E2
Solve for D%5B1%5D.
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The midpoint of BC is calculated using the points B and C.
It's the average of the x and y values.
M%5BBCx%5D=%2890%2B57.86%29%2F2=73.9
M%5BBCy%5D=%280%2B62.27%29%2F2=31.2
M%5BBC%5D=(73.9,31.2)
Again use the distance formula,
D%5B2%5D%5E2=%280-73.9%29%5E2%2B%280-31.2%29%5E2
Solve for D%5B2%5D.