a ladder is 22 ft long. the base of the ladder is 18 ft from the house. how high is the wall? round to the nearest tenth.

Question

homework help

Answer 1

Assuming that the house is perpenidcular to the ground on which the ladder stands, use the Pythagorean Theorem for the sides of right triangles:

           a² + b²  =  c²

In this problem a = 18, b is the unknown, and c is the length of the ladder (the hypotenuse of the triangle).

          18² + b²  =  22²   or

                     b²  =  22² - 18²

                     b²  =  484 - 324

                     b²  =  160

                     b    =  √160  =  12.6 ft.

(It would be hard to climb that ladder because it is farther away from the wall than the height of the place where it touches the house)

Answer 2

The best way to deal with these problems is to first make a sketch. The sketch should look like a triangle with the wall on the left of height (h), the ground at the bottom with the ladder forming the diagonal starting at the top of the wall and touching the ground at distance (d) from the wall. The diagonal length is L, or the length of the ladder. The pythagoream theorem can be used which would be L^2=h^2+d^2 in this case. To find h, re-arrange the formula to be h=sqrt(L^2-d^2). Substitute the given values to calculate h = SQRT(22^2-18^2) = 12.6 feet (rounded to nearest 10th). This ladder would be hard to climb as it's angle to the ground is too flat.

Answer 3

Yes, using the Pythagorean Theorem will be the best mathematical solution as listed above. If you do not understand it, try taking a piece of graph paper and make a triangle with the ladder and the distance from the house as the given number of blocks. Draw straight lines and make each block equal to one foot. Where the two lines meet (intersect) is the height of the wall. Count the blocks. You have then solved the problem with a graphic illustration and perhaps it helps you understand how the Pythagorean theorem works. I always look for the simplest graphic illustration for the problem and then apply the correct mathematical formula. I hope this helps.

Answer 4

Here we can use the Pythagorean Theorem: A²+B²=C²

Where C (hypotenuse) = 22; B (Base) = 18; A (Wall) = ?

Rewrite the theorem: A²=C²-B²

Substitute the given values: A²=22²-18²

Rewrite to solve for A: A=Squareroot(22²-18²)

Simplify: A=12.649 ft.

Round to the nearest 10^th: 12.6 ft.