Answer:
[tex]c = 14.9cm[/tex]
Step-by-step explanation:
Given
[tex]b = 10cm[/tex]
[tex]B = 12^{\circ}[/tex]
[tex]A = 150^{\circ}[/tex]
Required
Determine the length of c
First, we calculate C (the third angle of the triangle).
[tex]C = 180 - A - B[/tex]
[tex]C = 180 - 150 - 12[/tex]
[tex]C = 18^{\circ}[/tex]
Using Sine's law, we make use of:
[tex]\frac{sin\ B}{b} = \frac{sin C}{c}[/tex]
By substituting values, we have:
[tex]\frac{sin\ 12}{10} = \frac{sin 18}{c}[/tex]
Cross multiply
[tex]c* sin\ 12 = 10 * sin\ 18[/tex]
Make c the subject
[tex]c = \frac{10 * sin\ 18}{sin\ 12}[/tex]
[tex]c = \frac{10 * 0.3090}{0.2079}[/tex]
[tex]c = 14.9cm[/tex] approximated
