Question

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

Answer 1

`"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^@`