Answer:
n = √3
m = √3
Explanation:
The triangle is an isosceles right triangle with 2 equal base angles of 45° each.
Thus:
Reference angle = 45°
Hypotenuse = √6
Opposite = m
Adjacent = n
✔️To find m, apply the trigonometric function SOH, we have:
Sin 45 = opp/hyp
Sin 45 = m/√6
√6 × 1/√2 = m (sin 45 = 1/√2)
√6/√2 = m
√(6/2) = m
√3 = m
m = √3
✔️To find n, apply the trigonometric function, CAH:
Cos 45 = adj/hyp
Cos 45 = n/√6
√6 × √2/2 = n (cos 45 = √2/2)
√12/2 = n
√(4*3)/2 = n
(2√3)/2 = n
√3 = n
n = √3