Question

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

Answer 1

`m = 3√(2)`

`n = 3√(2)`

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*(1)/(√(2))` (sin 45 = 1/√2)

`m = (6)/(√(2))`

Rationalize

`m = (6*√(2))/(√(2)*√(2))`

`m = (6√(2))/(2)`

`m = 3√(2)`

✔️To find n, apply CAH:

Cos 45 = Adj/Hyp

Cos 45 = n/6

n = 6 × Cos 45

`n = 6*(1)/(√(2))` (cos 45 = 1/√2)

`n = (6)/(√(2))`

Rationalize

`n = (6*√(2))/(√(2)*√(2))`

`n = (6√(2))/(2)`

`n = 3√(2)`