Question

In a 45-45-90 triangle, if the length of one leg is 4, what is the length of the hypotenuse?​

Answer 1

Answer:
`4√(2)` (choice C)

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is found through this formula

`\text{hypotenuse} = \text{leg}√(2)`

We could also use the pythagorean theorem with a = 4, b = 4 to solve for c.

`a^2+b^2 = c^2\\\\c = √(a^2+b^2)\\\\c = √(4^2+4^2)\\\\c = √(2*4^2)\\\\c = √(2)*√(4^2)\\\\c = √(2)*4\\\\c = 4√(2)\\\\`