Question

Trig need help! Find the two missing sides and write your answer as in simplified radical form.

Answer 1

Answer:

$m = 3\sqrt{2}$

$n = 3\sqrt{2}$

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

$m = 6*\frac{1}{\sqrt{2}}$ (sin 45 = 1/√2)

$m = \frac{6}{\sqrt{2}}$

Rationalize

$m = \frac{6*\sqrt{2}}{\sqrt{2}*\sqrt{2}}$

$m = \frac{6\sqrt{2}}{2}$

$m = 3\sqrt{2}$

✔️To find n, apply CAH:

Cos 45 = Adj/Hyp

Cos 45 = n/6

n = 6 × Cos 45

$n = 6*\frac{1}{\sqrt{2}}$ (cos 45 = 1/√2)

$n = \frac{6}{\sqrt{2}}$

Rationalize

$n = \frac{6*\sqrt{2}}{\sqrt{2}*\sqrt{2}}$

$n = \frac{6\sqrt{2}}{2}$

$n = 3\sqrt{2}$