SOLUTION: I need to solve the triangle using the labels. I also need to round lengths of the sides to three sig digits and angles to the nearest tenth of a degree. A = ? B= ? C = 108.5

Algebra ->  Trigonometry-basics -> SOLUTION: I need to solve the triangle using the labels. I also need to round lengths of the sides to three sig digits and angles to the nearest tenth of a degree. A = ? B= ? C = 108.5       Log On


   

Question 525332: I need to solve the triangle using the labels. I also need to round lengths of the sides to three sig digits and angles to the nearest tenth of a degree.
A = ?
B= ?
C = 108.5
a= 415 m
b = 325 m
c = ?
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

 

c² = a² + b² - 2ab·cos(C)
c² = 415² + 325² - 2(415)(325)cos(108.5°)
c² = 363442.9311
 c = 602.862282m

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

c·sin(A) = a·sin(C)

sin(A) = %28a%2Asin%28C%29%29%2Fc

sin(A) = %28415%2Asin%28108.5%29%29%2F602.862282

sin(A) = .6528096526

    A = 40.75377413°

A + B + C = 180°
        B = 180° - A - C
        B = 180° - 40.75377413° - 108.5°
        B = 30.74622587°

A = 40.8°
B = 30.7° 
C = 108.5
a = 415m
b = 325m
c = 603m

Edwin