SOLUTION: if ∠A =26,∠c= 24,b=15 solve ΔABC

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Question 827223: if ∠A =26,∠c= 24,b=15 solve ΔABC
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


First we find ∠B 

  ∠A + ∠B + ∠C = 180°
24° + ∠B + 26° = 180°
      50° + ∠B = 180°
            ∠B = 130° 



Next we use the law of sines:

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

We fill in what we know:

a%2Fsin%28%2226%B0%22%29%22%22=%22%2215%2Fsin%28%22130%B0%22%29%22%22=%22%22c%2Fsin%28%2224%B0%22%29

We use the first and second parts of the law of sines to find side "a":

a%2Fsin%28%2226%B0%22%29%22%22=%22%2215%2Fsin%28%22130%B0%22%29

Cross-multiply:

a·sin(130°) = 15·sin(26°)

Divide both sides by sin(130°)

a%22%22=%22%2215sin%28%2226%B0%22%29%2Fsin%28%22130%B0%22%29

Use calculator

a = 8.583793357  (round as your teacher instructed, probably 8.6)

-----

We use the second and third parts of the law of cosines to find side "c":

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

15%2Fsin%28%22130%B0%22%29%22%22=%22%22c%2Fsin%28%2224%B0%22%29

Cross-multiply:

c·sin(130°) = 15·sin(24°)

Divide both sides by sin(130°)

c%22%22=%22%2215sin%28%2224%B0%22%29%2Fsin%28%22130%B0%22%29

Use calculator

c = 7.964354681  (round as your teacher instructed, probably 8.0)

Edwin