SOLUTION: Consider a triangle ABC. Supposed that A = 42 degrees, C = 37 degrees, and b = 31. (Figure not drawn to scale. Solve the triangle. Round your answer to the nearest tenth. I

Algebra ->  Test -> SOLUTION: Consider a triangle ABC. Supposed that A = 42 degrees, C = 37 degrees, and b = 31. (Figure not drawn to scale. Solve the triangle. Round your answer to the nearest tenth. I      Log On


   

Question 1037897: Consider a triangle ABC. Supposed that A = 42 degrees,
C = 37 degrees, and b = 31. (Figure not drawn to scale.
Solve the triangle.
Round your answer to the nearest tenth. If there
is more than one solution, use the "or"
B = ? degrees
a = ?
c = ?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

This one IS drawn to scale! :)  Measure the angles and see!

  

First we find angle B:

    A + B + C = 180°
42° + B + 37° = 180°
      79° + B = 180°
            B = 101°

Use the law of sines:

a%2Fsin%28A%29%22%22=%22%22b%2Fsin%28B%29%22%22=%22%22c%2Fsin%28C%29

a%2Fsin%28%2242%B0%22%29%22%22=%22%2231%2Fsin%28%22101%B0%22%29%22%22=%22%22c%2Fsin%28%2237%B0%22%29

Taking the first two:

a%2Fsin%28%2242%B0%22%29%22%22=%22%2231%2Fsin%28%22101%B0%22%29

a%22%22=%22%2231sin%28%2242%B0%22%29%2Fsin%28%22101%B0%22%29

a%22%22=%22%2231sin%28%2242%B0%22%29%2Fsin%28%22101%B0%22%29

a%22%22=%22%2221.13129011

Taking the last two:

31%2Fsin%28%22101%B0%22%29%22%22=%22%22c%2Fsin%28%2237%B0%22%29

%2831sin%28%2237%B0%22%29%29%2Fsin%28%22101%B0%22%29%22%22=%22%22c

19.00544935%22%22=%22%22c

You can round to nearest tenth!  :)

Edwin