Question

In △ABC, m∠A=55°, c=11, and m∠B=19°. Find the perimeter of the triangle.law of sines 4A. 39B. 24C. 32D. 48

Answer 1

Solution: 24.096

Analysis:

We have a triangle and know two angles and one side of the triangle. According to the angle rule, a triangle's total intern angles equals 180 degrees. We have:

mm∠B=19°

∠A+∠B+∠C=180°

55°+19°+∠C=180°

∠C=180°-55°-19°

∠C=106°

`(a)/(sin(A))=(b)/(sin(B))=(c)/(sin(C))`
`\begin{gathered} (a)/(sin(55))=(11)/(sin(106)) \\ \\ a=(11\ast sin(55))/(sin(106))=(11\ast0.82)/(0.96)=9.37 \end{gathered}`

`\begin{gathered} (b)/(sin(19))=(11)/(sin(106)) \\ \\ b=(11\ast sin(19))/(sin(106))=(11\ast0.325)/(0.96)=3.726 \end{gathered}`

Perimeter=a+b+c

Perimeter=9.37+3.726+11

Perimeter=24.096