Question

A ladder is leaning against a wall to form a triangle with the ground and the wall. the length of the ladder is 12 feet. the distance from the wall to the base of the ladder is 6 startroot 2 endroot feet. the wall and the floor form a right angle. 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 startroot 2 endroot 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:startroot 2 endroot. the leg-to-hypotenuse ratio is 1:startfraction startroot 2 endroot over 2 endroot. the nonright angles are congruent. the ladder represents the longest length in the triangle.

Answer 1

The correct options are:

1) the triangle is isosceles.

2) the leg-to-hypotenuse ratio is 1:√2  

3) the non-right angles are congruent.

4) the ladder represents the longest length in the triangle.

For given question,

the length of the ladder is 12 feet.

the distance from the wall to the base of the ladder is 6√2 feet

Let x be the height of the wall.

Using Pythagoras theorem,

⇒ x² + (6√2)² = 12²

⇒ x² = 72

⇒ x = 8.5 ft

So, the triangle is right triangle.

Here, the hypotenuse = 12 ft

And, the leg-to-hypotenuse ratio is,

6√2 : 12 = 1:√2

We know that the right triangle is an isosceles triangle.

Since the right triangle is an isosceles  triangle, the non-right angles are congruent.

We know that, the hypotenuse is the longest length in the triangle.

So, the ladder represents the longest length in the triangle.

Therefore, the correct options are:

1) the triangle is isosceles.

2) the leg-to-hypotenuse ratio is 1:√2  

3) the non-right angles are congruent.

4) the ladder represents the longest length in the triangle.

Learn more about the right triangle here:

https://brainly.com/question/6322314

#SPJ4