Given:
[tex]\begin{gathered} \angle a=30\degree \\ c=5 \end{gathered}[/tex]
Required:
To find the missing information.
Explanation:
Since ABC is a right angle triangle.
[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 30\degree+90\degree+\angle C=180\degree \\ 120\degree+\angle C=180\degree \\ \angle C=180\degree-120\degree \\ \angle C=60\degree \end{gathered}[/tex]
Now by using the trigonometric ratios we will find the values of a and b.
[tex]\begin{gathered} cos\theta=\frac{adj.}{hyp.} \\ cos30\degree=\frac{5}{b} \\ \frac{\sqrt{3}}{2}=\frac{5}{b} \\ b=\frac{10}{\sqrt{3}} \\ b=\frac{10}{1.732} \\ b=5.77 \\ b\approx5.8 \end{gathered}[/tex]
[tex]\begin{gathered} tan\theta=\frac{opp.}{adj.} \\ tan30\degree=\frac{a}{5} \\ \frac{1}{\sqrt{3}}=\frac{5}{a} \\ a=5\sqrt{3} \\ a=5(1.732) \\ a=8.66 \\ a\approx8.7 \end{gathered}[/tex]
Final answer:
[tex]\begin{gathered} a=8.7 \\ b=5.8 \\ \angle C=60\degree \end{gathered}[/tex]
