The bottom of a ladder must be placed 3 ft. from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall?

Answer 1

The ladder leaning up against the wall forms a right triangle so you can use the Pythagorean to find the height, the missing side

a² + b² = c²

b = 3 ft the distance from ladder to wall on ground the base of your triangle

c = 12 ft the length of the ladder laid diagonally from a point on the wall to the ground and the longest side

a = height how far above the ground the ladder touches the wall

Rearranging the equation to solve for a²

a² + b² = c²

c² - b² = a²

SQRT(c² - b²) = a

SQRT(12² - 3²) = a

SQRT(144 - 9) = a

SQRT(135) = a

√9 *√15= a

3*√15 = a

11.6 = a

I hope you find this useful if you any questions send me a message.

Answer 2

The ladder question is a popular one for studying the geometry of triangles. The ladder leaning against the wall forms the hypotenuse of a right triangle (c in this case). The distance of the base from the wall is your short side (a), and you want to calculate the long side (b).

c^2 = a^2 + b^2

144 = 9 + b^2

135 = b^2

The distance up the wall (b) is about 11.6 ft.