Given:-
An image with triangle.
To find:-
The value of B,a,c.
So the laws of sines are,
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
So now we substitute the known values. we get,
[tex]\frac{\sin16}{a}=\frac{\sin B}{5.1}=\frac{\sin125}{c}[/tex]
Now we find the value of B,
Since the sum of angles of the triangle is 180. we get,
[tex]\begin{gathered} A+B+C=180 \\ 16+B+125=180 \\ B+141=180 \\ B=180-141 \\ B=39 \end{gathered}[/tex]
So substituting the value we get,
[tex]\frac{\sin16}{a}=\frac{\sin 39}{5.1}=\frac{\sin125}{c}[/tex]
Now we find the value of a. we get,
[tex]\begin{gathered} \frac{\sin16}{a}=\frac{\sin 39}{5.1} \\ \frac{0.2756}{a}=\frac{0.6293}{5.1} \\ a=\frac{0.2756\times5.1}{0.6293} \\ a=2.2335 \end{gathered}[/tex]
Now we find c. we get,
[tex]\frac{0.2756}{2.2335}=\frac{\sin 125}{c}[/tex]
So
