Answer:
[tex] m = 3\sqrt{2} [/tex]
[tex] n = 3\sqrt{2} [/tex]
Step-by-step explanation:
Reference angle = 45°
Opposite = m
Adjacent = n
Hypotenuse = 6
✔️To find m, apply SOH:
Sin 45 = Opp/Hyp
Sin 45 = m/6
m = 6 × Sin 45
[tex] m = 6*\frac{1}{\sqrt{2}} [/tex] (sin 45 = 1/√2)
[tex] m = \frac{6}{\sqrt{2}} [/tex]
Rationalize
[tex] m = \frac{6*\sqrt{2}}{\sqrt{2}*\sqrt{2}} [/tex]
[tex] m = \frac{6\sqrt{2}}{2} [/tex]
[tex] m = 3\sqrt{2} [/tex]
✔️To find n, apply CAH:
Cos 45 = Adj/Hyp
Cos 45 = n/6
n = 6 × Cos 45
[tex] n = 6*\frac{1}{\sqrt{2}} [/tex] (cos 45 = 1/√2)
[tex] n = \frac{6}{\sqrt{2}} [/tex]
Rationalize
[tex] n = \frac{6*\sqrt{2}}{\sqrt{2}*\sqrt{2}} [/tex]
[tex] n = \frac{6\sqrt{2}}{2} [/tex]
[tex] n = 3\sqrt{2} [/tex]
