Question

Solve the triangle: a=63, =93,6=83. If it is not possible, say so.This triangle is not solvable.a=77.8.8= 60.7.y=41.5=41.5.6=77.8.y=60.7a = 607.6= 415.y=77.8

Answer 1

It is given that

$a=6.3,b=9.3,c=8.3$

Use the cosine rule to get:

$\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{(9.3)^2+(8.3)^2-(6.3)^2}{2\ast9.3\ast8.3}=0.7493 \\ A=\cos ^{-1}(0.7493)=41.46\approx41.5^{\circ} \end{gathered}$

Similarly for angle B it follows:

$\begin{gathered} \cos B=\frac{a^2+c^2-b^2}{2ac}=\frac{(6.3)^2+(8.3)^2-(9.3)^2}{2\ast6.3\ast8.3}=\frac{2209}{10458} \\ B=\cos ^{-1}(\frac{2209}{10458})=77.8^{\circ} \end{gathered}$

The value for angle C is given by the formula

$\begin{gathered} A+B+C=180 \\ C=180-B-A \\ C=180-77.8-41.5=60.7^{\circ} \end{gathered}$

Hence option C is correct.