using the 45 -45 -90 triangle theorem find the exact value of all the missing sides with a triangle - leg is x, leg is 5, and hypotenuse is 5 square root of 2

Answer 1

Using the 45-45-90 triangle theorem, we know that in a triangle where the two legs are congruent, the hypotenuse is √2 times the length of the legs.

Given that the leg is x, the other leg is 5, and the hypotenuse is 5√2, we have:

leg (x) = 5
hypotenuse = 5√2

From the theorem, we can find the length of the missing leg (x) by using the formula:

leg = hypotenuse / √2

Plugging in the values:

x = 5√2 / √2
x = 5

So the missing leg in the triangle is also 5.