Question 1143241: If angle C = 70 degrees, angle A = 45 degrees and AB = 40 m. What is the length of the median drawn from the vertex A to side BC. Thank you.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let median(BC) be the length of the median drawn from angle A to side BC, then
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BC = (1/2) * square root(2 * AB^2 + 2 * AC^2 - BC^2)
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Use the Law of Sines to find the length of the other two sides
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Note angle A = 45 degrees, angle C = 70 degrees, then angle B = 65 degrees
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The problem states that AB = 40m, then
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40/sin(70) = BC/sin(45)
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BC = (sin(45) * 40)/sin(70) = 30.0995
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40/sin(70) = AC/sin(65)
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AC = (sin(65) * 40)/sin(70) = 38.5789
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median(BC) = (1/2) * square root(2 * (40)^2 + 2 * (38.5789)^2 - (30.0995)^2) = 36.2997
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The length of the median(BC) is approximately 36.3m
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