Question

Choose all situations that describe a right triangle.

A ladder 12 feet long leans against a wall. The top of the ladder is 8 feet above the ground. The bottom of the ladder is 6 feet from the wall.


A ladder 10 feet long leans against a wall. The top of the ladder is 6 feet above the ground. The bottom of the ladder is 8 feet from the wall.


A ladder 18 feet long leans against a wall. The top of the ladder is 9 feet above the ground. The bottom of the ladder is 12 feet from the wall.


A ladder 15 feet long leans against a wall. The top of the ladder is 12 feet above the ground. The bottom of the ladder is 9 feet from the wall.

Answer 1

We have a right triangle in cases 2 and 4

Explanation:

In a right, we have to meet the condition of Pythagoras´ Theorem that is

L² = x² + y² ( L is the hypotenuse and "x" and "y" the legs.

All the above descriptions have a right angle so we must check which of them meet Pythagoras´theorem requirement

1.-

(12)² = (8)² + (6)² ⇒ 144 > 64 + 36 so in this case we do not have a right triangle

2.-

(10)² = (6)² + (8)² ⇒ 100 = 36 + 64 We have here a description of a right triangle

3.-

(18)² = (9)² + (12)² ⇒ 324 > 81 + 144 so in this case we do not have a right triangle

4.-

(15)² = (12)² + (9)² ⇒ 225 = 144 + 81 We have here a description of a right triangle´