Question

What is the perimeter p of triangle ABC to the nearest whole number?

Answer 1

Find the missing angle of the triangle

`\begin{gathered} A=180-40-49 \\ A=180-89 \\ A=91 \end{gathered}`

apply the law of sines in order to find the missing sides

`\begin{gathered} (26)/(\sin49)=(c)/(\sin 40) \\ b=26\cdot(\sin40)/(\sin49) \\ b\cong22.14 \end{gathered}`

`\begin{gathered} (26)/(\sin49)=(a)/(\sin 91) \\ a=26\cdot(\sin 91)/(\sin 49) \\ a\cong34.33 \end{gathered}`

add the three sides to find the perimeter

`\begin{gathered} P=26+34.33+22.14 \\ P=82.47\cong82 \end{gathered}`