SOLUTION: The perimeter of a triangle ABC is 400 cm. if angle A is 30 degree and angle B is 58 degree. Find the measure of side AC.

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Question 766551: The perimeter of a triangle ABC is 400 cm. if angle A is 30 degree and angle B is 58 degree. Find the measure of side AC.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A drawing would be according to angle at C is 92 degrees. Side length opposite A is a; side length opposite B is b; side length opposite C is c.

Given perimeter means a%2Bb%2Bc=400.
Law of Sines gives:
sin%2830%29%2Fa=sin%2858%29%2Fb
sin%2858%29%2Fb=sin%2892%29%2Fc
sin%2830%29%2Fa=sin%2892%29%2Fc
A couple more equations that come from them are:
b=a%2Asin%2858%29%2Fsin%2830%29 and c=b%2Asin%2892%29%2Fsin%2858%29

Use those last two to substitute into the perimeter.
Also make use of the b= equation again since b still shows in this substitution.

.some couple steps..
.calculator or table of trigonometric function values...
a%2A%284.6949%29=400
highlight%28a=85.1992%29

From that, other simpler law of sine relationships give highlight%28b=144.506%29 and highlight%28c=170.2948%29