SOLUTION: Two angles of an oblique triangle are 60 and 50 degrees and their included side is 400 cm long. Find the area. Use sine law to determine the remaining sides.

Question 1150861: Two angles of an oblique triangle are 60 and 50 degrees and their included side is 400 cm long. Find the area. Use sine law to determine the remaining sides.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
An oblique triangle is any triangle that is not a right triangle.
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The third angle of the given triangle is 180 -(60+50) = 70 degrees
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using the law of sines
:
400/sin(70) = x/sin(50)
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cross-multiply fractions and solve for x
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x = (400 * sin(50))/sin(70) = 326.083
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400/sin(70) = x/sin(60)
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x = (400 * sin(60))/sin(70) = 368.642
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the three sides are 400, 326.083 and 368.642
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use Heron's formula to calculate the area of the triangle
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s = (400 +326.083 +368.642)/2 = 547.3625
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Area of triangle = square root(547.3625 * (547.3625-400) * (547.3625 - 326.083) * (547.3625 - 368.642)) = 56479.2325
:
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Area of triangle is 56479.2325 square cm
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