Answer/Step-by-step explanation:
✔️Find k:
Reference angle = 60°
Hypotenuse = k
Opposite = 9
Therefore, using trigonometric ratio, we have:
[tex] sin(60) = \frac{9}{k} [/tex]
Multiply both sides by k
[tex] k*sin(60) = 9 [/tex]
Divide both sides by sin(60)
[tex] k = \frac{9}{sin(60)} [/tex]
[tex] k = \frac{9}{\frac{\sqrt{3}}{2}} [/tex]
[tex] k = 9*\frac{2}{\sqrt{3}} [/tex]
[tex] k = \frac{18}{\sqrt{3}} [/tex]
Rationalize
[tex] k = \frac{18*\sqrt{3}}{\sqrt{3}*\sqrt{3}} [/tex]
[tex] k = \frac{18\sqrt{3}}{3} [/tex]
[tex] k = 6\sqrt{3} [/tex]
✔️Find f:
Reference angle = 60°
Opposite = 9
Adjacent = f
Therefore, using trigonometric ratio, we have:
[tex] tan(60) = \frac{9}{f} [/tex]
Multiply both sides by f
[tex] f*tan(60) = 9 [/tex]
Divide both sides by tan(60)
[tex] f = \frac{9}{tan(60)} [/tex]
[tex] k = \frac{9}{\sqrt{3}} [/tex]
Rationalize
[tex] k = \frac{9*\sqrt{3}}{\sqrt{3}*\sqrt{3}} [/tex]
[tex] k = \frac{9\sqrt{3}}{3} [/tex]
[tex] k = 3\sqrt{3} [/tex]
