SOLUTION: This problem refers to triangle ABC. If b = 4.7 m, c = 6.6 m, and A = 118°, find a. (Round your answer to one decimal place.) a = m

Algebra ->  Triangles -> SOLUTION: This problem refers to triangle ABC. If b = 4.7 m, c = 6.6 m, and A = 118°, find a. (Round your answer to one decimal place.) a = m      Log On


   

Question 1135789: This problem refers to triangle ABC.
If b = 4.7 m, c = 6.6 m, and A = 118°, find a. (Round your answer to one decimal place.)
a = m
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Do NOT post this.
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a = m

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Given Values:
b = 4.7
c = 6.6
Angle A = 118 is between sides b and c

The placement of A between b and c is important, as it means we have a SAS (side angle side) case going on here. When it comes to SAS like this, we'll use the Law of Cosines.

Use the Law of Cosines to solve for side 'a'
a^2 = b^2 + c^2 - 2*b*c*cos(A)
a^2 = 4.7^2 + 6.6^2 - 2*4.7*6.6*cos(118)
a^2 = 22.09 + 43.56 - 62.04*cos(118)
a^2 = 22.09 + 43.56 - 62.04*(-0.469471562785891)
a^2 = 22.09 + 43.56 - (-29.1260157552366)
a^2 = 22.09 + 43.56 + 29.1260157552366
a^2 = 94.7760157552367
a = sqrt(94.7760157552367)
a = 9.7352974148321

Rounded to one decimal place, the final answer is a = 9.7