Question 921008: Find the lengths of all three sides of a right triangle that has perimeter 35 and has a 35 degree angle. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find the lengths of all three sides of a right triangle that has perimeter 35 and has a 35 degree angle.
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The other acute angle is 65 degrees
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Let side opposite the 35 degree angle be "a"
Let side opposite the 65 degree angle be "b"
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a/sin(35) = b/sin(65)
0.5736b = 0.9063a
a/b = 0.5736/0.9063 = 0.6329
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a = 0.6329b
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a^2 + b^2 = c^2
(0.6329b)^2 + b^2 = c^2
0.4006b^2 + b^2 = c^2
1.4006b^2 = c^2
c^2/b^2 = 1/1.4006
c/b = 1.1835
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c = 1.1835b
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Note: a + b + c = 35 (given)
0.6329b + b +1.1835b = 35
2.8164b = 35
b = 12.43
a = 0.6329b = 0.6329*12.43 = 7.8653
c = 1.1835b = 1.1835*12.43 = 14.71
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Cheers,
Stan H.
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