SOLUTION: Solve the given triangle. A = 50 degrees, B = 50 degrees, c = 12 meters Round your answers to the nearest integer. C = ? degrees b = ? meters c = ? meters

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Question 620858: Solve the given triangle. A = 50 degrees, B = 50 degrees, c = 12 meters
Round your answers to the nearest integer.
C = ? degrees
b = ? meters
c = ? meters



Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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You can solve this problem by using the Angle Sum Theorem for triangles, and the Law of Sines.
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STEP I: Find the measure of angle C.
The Angle Sum Theorem states the the sum of the measures of the interior angles of any triangle is 180 degrees.
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Add the measure of angle A to that of angle B. (50+50=100). Subtract this value from 180. (180-100=80). The measure of angle C is 80 degrees.
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STEP II: Find the missing side lengths of triangle ABC.
The Law of Sines states that the follow proportions hold true.
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sin%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc
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Substitute the values you are given for each value. Solve for a and b to find the missing side lengths.
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(NOTE: You may have a typo in your problem, since the length of c is given and the show the problem asking for the length of c. No worries...if the problem is typed incorrectly, follow my method with the correct values.)
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sin%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc
sin%2850%29%2Fa=sin%2850%29%2Fb=sin%2880%29%2F12
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Use a calculator to find the dine of each angle.
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0.766%2Fa=0.766%2Fb=0.985%2F12
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(You can carry this out to more decimal places if you choose to. We know sin(c) and length c, we can reduce this fraction to a decimal.
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0.985%2F12=0.082
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Now divide to find side a and side b.
a=0.766%2F0.082
a=9.341
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The side opposite angle A is 9.341 meters. Notice that a=b because angle A=angle B. This is an isosceles triangle, so the side opposite angle b is also 9.341 meters.
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Hope this helps. Feel free to email if you have questions about the solution.
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Ms.Figgy
math.in.the.vortex@gmail.com