Answer:
A.
[tex] x = \frac{7\sqrt{6}{3} [/tex]
[tex] y = \frac{7\sqrt{6}}{3} [/tex]
Step-by-step explanation:
Reference angle = 60°
Opposite = [tex] \frac{7\sqrt{2}}{2} [/tex]
Hypotenuse = x
Adjacent = y
✔️To find x, apply the trigonometric function SOH:
Sin 60° = Opp/Hyp
[tex] sin 60° = \frac{\frac{7\sqrt{2}}{2}}{x} [/tex]
[tex] \frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{2}}{2}}{x} [/tex] (sin 60 = √3/2)
[tex] \frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2}*\frac{1}{x} [/tex]
[tex] \frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2x} [/tex]
Cross multiply
[tex] \sqrt{3}*2x = 7\sqrt{2}*2 [/tex]
[tex] 2\sqrt{3}*x = 14\sqrt{2} [/tex]
Divide both sides by 2
[tex] \sqrt{3}*x = 7\sqrt{2} [/tex]
Divide both sides by √3
[tex] x = \frac{7\sqrt{2}}{\sqrt{3}} [/tex]
Rationalize
[tex] x = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}} [/tex]
[tex] x = \frac{7\sqrt{6}{3} [/tex]
✔️To find y, apply the trigonometric function TOA:
Tan 60° = Opp/Adjacent
[tex] Tan 60° = \frac{\frac{7\sqrt{2}}{2}}{y} [/tex]
[tex] \sqrt{3} = \frac{\frac{7\sqrt{2}}{2}}{y} [/tex] (tan 60 = √3)
[tex] \sqrt{3} = \frac{7\sqrt{2}}{2}*\frac{1}{y} [/tex]
[tex] \sqrt{3} = \frac{7\sqrt{2}}{2y} [/tex]
Cross multiply
[tex] \sqrt{3}*2y = 7\sqrt{2} [/tex]
[tex] 2\sqrt{3}*y = 7\sqrt{2} [/tex]
Divide both sides by √3
[tex] y = \frac{7\sqrt{2}}{\sqrt{3}} [/tex]
Rationalize
[tex] y = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}} [/tex]
[tex] y = \frac{7\sqrt{6}}{3} [/tex]
