ANSWER
[tex]\begin{gathered} (a)a=9.2 \\ (b)b=18.5 \\ (c)A=30\degree \end{gathered}[/tex]
EXPLANATION
(a) To find the value of a, we have to apply trigonometric ratios, SOHCAHTOA, for tangent for right triangles:
[tex]\tan 60=\frac{opposite}{adjacent}[/tex]
Therefore, we have that:
[tex]\begin{gathered} \tan 60=\frac{16}{a} \\ \Rightarrow a=\frac{16}{\tan 60} \\ a=9.2 \end{gathered}[/tex]
(b) To find the value of b, we have to apply trigonometric ratios, SOHCAHTOA, for sine for right triangles:
[tex]\sin 60=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Therefore, we have that:
[tex]\begin{gathered} \sin 60=\frac{16}{b} \\ \Rightarrow b=\frac{16}{\sin 60} \\ b=18.5 \end{gathered}[/tex]
(c) To find the measure of A, apply the total angle in a triangle.
The sum of angles in a triangle is 180 degrees. This implies that:
[tex]\begin{gathered} 90\degree+60\degree+A=180\degree \\ 150\degree+A=180 \\ \Rightarrow A=180\degree-150\degree \\ A=30\degree \end{gathered}[/tex]
