denise is using a ladder to clean the outside of her second story windows. the ladder she is using is 24 feet long and she puts the base of the ladder 13 feet away from the house in order to avoid her flower gardens. how high up the side of her house does the ladder reach? round to the nearest tenth, if necessary

First, always draw a diagram to help you solve the problem. (See the picture below). The situation forms a right triangle. We can assume the ground and the house and perpendicular, creating the 90° angle. The ladder is the hypotenuse.

Since we have a right triangle, and we have one missing side, we can solve the problem using the Pythagorean Theorem, which is a² + b² = c². "a" and "b" are the perpendicular sides and the "c" is the hypotenuse.

Assign a variable for the missing side (not the hypotenuse!)

let "b" represent the height the ladder reaches on the house

Use the formula and substitute the other known values. Then, isolate 'b' to solve by doing the reverse operations in the reverse order of BEDMAS.

a² + b² = c²

13² + b² = 24² Substitute the two known sides.

13² - 13² + b² = 24² - 13² Subtract 13² from both sides

b² = 24² - 13² Cancelled out positive 13² on the left side

√b² = √(24² - 13²) Square root both sides

b = √(24² - 13²) "b" is isolated because √ and ² are reverse operations

b = √(576 - 169) Square the numbers inside the bracket. Subtract.

b = √407 Find the square root

b = 20.174241 Round this number to nearest tenth

b ≈ 20.2 Answer in feet units

Remember when rounding, you round either up or down depending on the digit to the right of what you are rounding to.

"The nearest tenth" is rounding to the first decimal. To the right of the first decimal is '7'. Since '7' is "5 or greater" you round up. If '7' was "4 or less", you would round down.

Therefore, the ladder reaches 20.2 feet up the side of the house.