geometry question

Question

A 12-foot ladder leans against the side of a house with its base 3 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth.

Answer 1

-Assuming the house wall is perpendicular to the ground, the base of the right triangle is 3 feet long, the hypotenuse is 12 feet long, and the height is unknown. We will call the height "h".

-According to the Pythagorean Theorem, the square of the base plus the square of the height of a right triangle is equal to the square of the hypotenuse. This is shown in the equation: a² + b² = c² . Therefore 3² + h² = 12².

3² + h² = 12²

9 + h² = 144

h² = 144 - 9

h² = 135

h = the square root of 135

h = 11.62 (rounded to the nearest hundredth)

Answer 2

If you think about it, the ladder is creating a triangle with the house. The base of the triangle is 3ft and the hypotenuse of the triangle is 12ft.

The Pythagorean Theorem states for right triangles that the height, base and hypotenuse of a triangle are all related by a formula: height^2+base^2=hypotenuse^2. We need to find the height, so let us solve this equation for height: height=sqrt(hypotenuse^2-base^2).

Now plug in your values: height=sqrt(12^2 - 3^2)=11.62