Question

a 12 - foot ladder is leaning against a wall. the distance from the base of the wall to the base of the ladder is 6√2 feet. given this information, what can be determined about the triangle formed by the ground, wall, and ladder? check all that apply. the triangle is isosceles. the leg - to - hypotenuse ratio is 1:√2. the leg - to - hypotenuse ratio is 1:√2 / 2. the nonright angles are congruent. the ladder represents the longest length in the triangle.

Explanation:

Step1: Calculate leg - to - hypotenuse ratio

Let one leg $a = 6\sqrt{2}$ ft and hypotenuse $c = 12$ ft. Ratio is $\frac{a}{c}=\frac{6\sqrt{2}}{12}=\frac{\sqrt{2}}{2}$.

Step2: Check triangle properties

Using Pythagorean theorem to find other leg $b=\sqrt{c^{2}-a^{2}}=\sqrt{144 - 72}=\sqrt{72}=6\sqrt{2}$ ft. Since two legs are equal, it's isosceles. Non - right angles are congruent. Ladder is hypotenuse.

Answer:

The nonright angles are congruent., The leg - to - hypotenuse ratio is $\frac{\sqrt{2}}{2}$, The triangle is isosceles., The ladder represents the longest length in the triangle.