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=(b^2+c^2-a^2)/(2bc)=((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=(a^2+c^2-b^2)/(2ac)=((6.3)^2+(8.3)^2-(9.3)^2)/(2\ast6.3\ast8.3)=(2209)/(10458) \\ B=\cos ^(-1)((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.