Given:
In a right triangle at B,
[tex]\begin{gathered} a=3 \\ A=15^{\circ} \end{gathered}[/tex]
To find:
The length of the sides b and c and angle B.
Explanation:
Using the trigonometric ratio,
[tex]\begin{gathered} sinA=\frac{a}{c} \\ \sin15^{\circ}=\frac{3}{c} \\ c=\frac{3}{\sin15^{\circ}} \\ c=11.59 \\ c\approx11.6 \end{gathered}[/tex]
Using the trigonometric ratio,
[tex]\begin{gathered} \tan A=\frac{a}{b} \\ \tan15^{\circ}=\frac{3}{b} \\ b=\frac{3}{\tan15^{\circ}} \\ b=11.19 \\ b\approx11.2 \end{gathered}[/tex]
Using the angle sum property,
The angle B becomes,
[tex]\begin{gathered} 90+15+B=180 \\ B=180-90-15 \\ B=75^{\circ} \end{gathered}[/tex]
Final answer:
The values are,
[tex]\begin{gathered} b=11.2 \\ c=11.6 \\ B=75^{\circ} \end{gathered}[/tex]
