Question

What is the length of the hypotenuse of 45–45-90 triangle with legs of length 5 square root 3

Answer 1

length of hypotenuse (h) of 45-45-90 triangle with legs = 5sr3
The legs of a 45-45-90 triangle are equal since their opposite angles (45) are equal. The ratios for the sides of all 45-45-90 triangles is:
x, x, xsr2

`x \: across \: the \: 45s \: and \: x √(2) for \: h \\ so \: make \: x = 5 √(3)`

`then \: h = x √(2) = 5 √(3) * √(2) \\ h = 5 √(3 * 2) = 5 √(6)`