Question

A 52 foot ladder is set against the side of the house so that it reaches up 48 feet .if jevonte grabs the ladder at its base and pulls it 3 feet farther from the house ,how far up the side of the house will the ladder reach now ? (The answer is not 45ft) round to the nearest tenth of a foot
Please help my daughter is stuck and I can't figure it out thanks

Answer 1

Answer:

Step-by-step explanation:

The way to approach this that makes the most sense to a student would be to find out how far from the house the ladder currently is, then add 3 feet to that and do the problem all over again. This is right triangle stuff...Pythagorean's Theorem in particular. The ladder is the hypotenuse, 52 feet long. The height of the rectangle is the distance the ladder is up the side o the house, 48 feet. We plug those into Pythagorean's Theorem and solve for the distance the ladder is from the house:

$52^2=48^2+x^2$ and

$2704=2304+x^2$ and

$x^2=400$ so

x = 20. Now if we add the 3 feet that the ladder was pulled away from house, the distance from the base of the ladder to the house is 23 feet, the ladder is still 52 feet long, but what's different is the height of the ladder up the side of the house, our new x:

$52^2=23^2+x^2$ and

$2704=529+x^2$ and

$2175=x^2$ so

x = 46.6 feet