Question

In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5 in.? 25√ in. 52√ in. 5√ in. 55√ in.

Answer 1

The answer would be 25 because the slope ratio of 45 is 1

Answer 2

Answer:
`5√(2)\ in`

Explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.

Let H be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 5 in.

Now applying Pythagoras theorem, we get

`H^2=5^2+5^2=25+25\\\\\Rightarrow\ H^2=50\\\\\Rightarrow H=√(50)\\\\\Rightarrow H=5√(2)\ in`

Hence, the length of the hypotenuse =
`5√(2)\ in`