Question

10 fill in the blank 1 point in a 45 - 45 - 90 right triangle, what is the ratio of the length of one leg, to the length of the other leg? choose your answer... choose your answer... 1:1 2:1 radical 2:1 1: radical 2

Explanation:

Step1: Recall the properties of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 right triangle, the two legs are congruent (equal in length) because the two non - right angles are equal (both 45 degrees). Let the length of one leg be \(a\) and the length of the other leg be \(b\).

Step2: Calculate the ratio

The ratio of the length of one leg to the length of the other leg is \(\frac{a}{b}\). Since \(a = b\) (by the property of 45 - 45 - 90 triangle), \(\frac{a}{b}=\frac{a}{a}=1\) (assuming \(a
eq0\), and in a non - degenerate triangle \(a>0\)). So the ratio is \(1:1\).

Answer:

\(1:1\)