SOLUTION: 1.The sum of the sides of the triangle ABC is equal to 400 m. A = 38°, B = 58°. Find the side AC

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Question 1193132: 1.The sum of the sides of the triangle ABC is equal to 400 m. A = 38°, B = 58°. Find the side AC
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This may be not the best approach and is given as unfinished:
Draw and label the triangle.
x=AC
t=CB
By interior angles sum, the angle at C is 84 degrees.
400-x-t=AB

Try Law Of Sines for setting up at least two equations.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The law of sines says

a%2Fsin%28A%29=b%2Fsin%28B%29=c%2Fsin%28C%29

In words, that says that the ratio of the lengths of the 3 sides of the triangle is the same as the ratio of the sines of the 3 angles.

So find the lengths of the sides by dividing the perimeter into three parts in the ratio of the sines of the three angles.

sin%2838%29=0.61566
sin%2858%29=0.84805
sin%2884%29=0.99452

sin%2838%29%2Bsin%2858%29%2Bsin%2884%29=2.45823

400%2F2.45823=162.72

The side lengths are

162.72%2Asin%2838%29=100.18
162.72%2Asin%2858%29=137.99
162.72%2Asin%2884%29=161.83

CHECK:
100.18%2B137.99%2B161.83=400.00

AC is the side opposite angle B, which is the side of middle length, so

ANSWER: AC = 138 (rounded)