How do I find two sides of a right triangle with one given?

Question

Both unknowns are the same length and the hypotenuse is √72. How would I solve this?

Answer 1

sqr72 = 6sqr2, each of the two equal sides = (6/sqr2)/(sqr2) = 6

Use the Pythagorean Theorem

hypotenuse squared = 72 = s^2 + s^2 = 2s^2

s^2 = 72/2 = 36

s = sqr36 = 6 = length of each of the two equal sides

It's a 45-45 -90 degree right triangle

hypotenuse = h, opposite side = s

sin45 = s/h = s/sqr72

s =sqr72sin45 = sqr72/(sqr2/2) = 6sqr2/(sqr2/2) = 6

s=6