Question

If A=40°, B= 60° and a=12 cm find b.

Answer 1

I will draw the triangle to show the given information

To find b we will use the sine rule

$\frac{a}{\sin A}=\frac{b}{\sin B}$

Since a = 12

Since < A = 40 degrees

Since

Substitute them in the rule above

$\frac{12}{\sin40}=\frac{b}{\sin 60}$

By using the cross multiplication

$\begin{gathered} b\times\sin 40=12\times\sin 60 \\ b\sin 40=12\sin 60 \end{gathered}$

Divide both sides by sin 40

$\begin{gathered} \frac{b\sin40}{\sin40}=\frac{12\sin 60}{\sin 40} \\ b=16.16755626 \end{gathered}$

The value of b is about 16.17 cm to the nearest 2 decimal places