Answer: [tex]\sin C=\sin(60^{\circ})=\frac{\sqrt{3}}{2}[/tex]
[tex]\tan C=\tan(60^{\circ})=\sqrt{3}[/tex]
[tex]\sin B=\sin(30^{\circ})=\frac{1}{2}[/tex]
Step-by-step explanation:
In the given triangle ABC
∠A = 90°
∠B= 30°
∠C= 60°
AC=9
BC=18
By using trigonometric function values for the given angles, we have
The value of [tex]\sin C=\sin(60^{\circ})=\frac{\sqrt{3}}{2}[/tex]
The value of [tex]\cos B=\cos(30^{\circ})=\frac{\sqrt{3}}{2}\neq\frac{\sqrt{2}}{3}[/tex]
The value of [tex]\tan C=\tan(60^{\circ})=\sqrt{3}[/tex]
The value of [tex]\sin B=\sin(30^{\circ})=\frac{1}{2}[/tex]
The value of [tex]\tan B=\tan(30^{\circ})=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\neq\frac{2\sqrt{3}}{3}[/tex]
