The Ladder

Part of the Triangles section of Coddy's Geometry journey. Lesson 36 of 71.

A ladder leaning against a wall makes a right triangle. The wall and the ground meet at a right angle, and the ladder is the hypotenuse. A ladder of length 5 with its foot 3 from the wall reaches a height h up the wall. To find h, subtract the square of the ground distance from the square of the ladder and take the root:

$A right triangle with the wall as one leg h, the ground as the other leg 3 and the ladder as the hypotenuse 5$

A ladder of 5, its foot 3 from the wall

h = √(5^2 - 3^2)

h = √(25 - 9) = √(16) = 4

The ladder reaches 4 up the wall.

The ladder is opposite the right angle between the wall and the ground, so it is the hypotenuse. To find the height, subtract the square of the distance along the ground from the square of the ladder's length, then take the positive square root. The height must be less than the length of the ladder. If your answer is longer than the ladder, you have made a mistake.