Question

question 2 of 25
in a 45-45-90 right triangle, what is the ratio of the length of one leg to the
length of the other leg?

a. \\( \sqrt{2}:1 \\)

b. \\( 1:1 \\)

c. \\( 1:\sqrt{2} \\)

d. \\( 2:1 \\)

Explanation:

Step1: Recall 45-45-90 triangle properties

In a 45-45-90 right triangle, the two acute angles are equal (both 45°). By the Isosceles Triangle Theorem, the sides opposite equal angles are equal. The legs of a right triangle are the sides opposite the acute angles. So, the two legs (opposite the 45° angles) are equal in length.

Step2: Determine the ratio

Let the length of one leg be \( a \) and the other leg be \( b \). Since the legs are equal, \( a = b \). The ratio of one leg to the other leg is \( \frac{a}{b}=\frac{a}{a} = 1\) (or \( a:b = 1:1 \)).

Answer:

B. 1:1