Solving this triangle?

Please determine which law of sines applies, then solve the triangle

a=3.3
b=2.1
c=2.7

Thanks guys

1 Answer
Jim G.
Dec 3, 2017

#"see explanation"#

Explanation:

#"since all 3 sides of the triangle are given"#

#"we can find the angles using the "color(blue)"cosine rule"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(cosA=(b^2+c^2-a^2)/(2bc))color(white)(2/2)|)))#

#rArrangleA=cos^-1((2.1^2+2.7^2-3.3^2)/(2xx2.1xx2.7))=85.9^@#

#"similarly note the pattern"#

#•color(white)(x)cosB=(a^2+c^2-b^2)/(2ac)#

#rArrangleB=cos^-1((3.3^2+2.7^2-2.1^2)/(2xx3.3xx2.7))=39.4^@#

#•color(white)(x)cosC=(a^2+b^2-c^2)/(2ab)#

#rArrangleC=cos^-1((3.3^2+2.1^2-2.7^2)/(2xx3.3xx2.1))=54.7^@#

#color(blue)"As a check"#

#angleA+angleB+angleC=85.9+39.4+54.7=180^@#

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