Question

A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?

Answer 1

One side length is equal to `sqrt(98)`.

Explanation:

We can start off by establishing that this triangle is a right, isosceles triangle. We can say this because of the converse of the isosceles triangle theorem, which states if two angles are congruent, then then 2 sides are congruent.

What we can conclude from the previous statement, is that the two legs are equal length. Therefore, we can use a modified version of the Pythagorean Theorem. That is, since `a ~= b`, we can substitute `a` in for `b`. That makes our equation `a^2 + a^2 = c^2`.

We know that the hypotenuse is `14`, so we can plug that into the equation. `a^2 + a^2 = 14^2 => 2a^2 = 196`. We can divide each side by 2, and square root each side to rid of the exponent.

That leaves us with `a = sqrt(98).`