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91Ó°ÊÓ

Solve the triangle

a = 3, b = 4, C = 40°

Short Answer

Expert verified

The solution is

c=2.55,A=48.7°,B=91.3°

Step by step solution

01

Step1. Given information

a=3,b=4,C=40°

02

Step2. Formula used

c2=a2+b2-2ab.cosC,cosA=b2+c2-a22bc

03

Step3. Calculation

Weknowc2=a2+b2-2ab.cosC=32+42-2.3.4.cos40°=9+16-24..77=25-18.48=6.52c=6.52=2.55Again,cosA=b2+c2-a22bc=42+2.552-322.4.2.55=16+6.52-920.4=13.5220.4=.66A=cos-1.66=48.7°weknow,A+B+C=180°48.7°+B+40°=180°B=180°-88.7°=91.3°

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