Question

Question #54875

Answer 1

see explanation.

Explanation:

By the Law of Cosines, we know that:
`c^2=a^2+b^2-2*a*b*cosangleC`
Putting in the values, we get
`9^2=4^2+7^2-2*4*7*cosangleC`
`=> cosangleC = (16+49-81)/(2*4*7)=-0.28571`
`=> angleC=cos^-1(-0.28571)=106.60^@`

Similarly,
`a^2=b^2+c^2-2*b*c*cosangleA`
`=> cosangleA=(9^2+7^2-4^2)/(2*9*7)=0.90476`
`=> angleA=cos^-1(0.90476)=25.21^@`

`=> angleB=180-angleC-angleA=180-106.60-25.21=48.19^@`