Question

The hypotenuse of a 45°-45°-90° triangle measures 22 square root 2 units

Answer 1

hypotenuse = 22*sq root (2)
I'm guessing you need to know the length of the triangle legs?
The triangle leg of a 45 45 90 triangle = hypotenuse / sq root (2)
triangle leg= 22* sq root (2) / sq root (2)
triangle leg=22

Answer 2

22units

Explanation:

Using the SOH CAH TOA method to solve the problem since the triangle is a 45°-45°-90° triangle which is a right angled triangle due to the presence of 90° as one or the angles.

If one of the sides is 22√2units,

Using SOH which states;

sin(theta) = Opposite/Hypotenuse

theta =45° (the angle facing one of the acute angle in the triangle)

Opposite side = 22√2

Substituting the datas into the formula we will have;

Sin 45° = 22√2/Hyp

1/√2 = (22√2)/Hyp

Cross multiplying;

Hypotenuse = √2×22/√2

Hypotenuse = 22units