Answer:
24.0 cm
Explanation:
To find the value of a, we will use the Law of sines, so
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]
So, replacing A = 150°, B = 12°, and b = 10 cm, we get:
[tex]\frac{\sin150}{a}=\frac{\sin 12}{10}[/tex]
Now, we need to solve for a. First, cross multiply
[tex]10\cdot\sin 150=a\cdot\sin 12[/tex]
Then, divide by sin12
[tex]\begin{gathered} \frac{10\cdot\sin150}{\sin12}=\frac{a\cdot\sin 12}{\sin 12} \\ \frac{10\cdot(0.5)}{0.208}=a \\ 24.0=a \end{gathered}[/tex]
Therefore, a = 24.0 cm
