1. Pythagorean Theorem Practice Problems More Challenging!

2. Problem 1 Solve for the missing side of the triangle.

3. Solution The missing side has length ~6.08. Using the Pythagorean Theorem, a 2 +b 2 =c 2. The missing side, since it’s the hypotenuse, has length c. Plugging in known values: 20 + 17 = c 2. Simplify. c 2 = 37 Take the square root of both sides of the equation. c ≈ 6.08

4. Problem 2 Bob has a 15 foot long ladder. The instructions for the ladder tell him that he should put the base at least 8 feet away from the base of whatever he’s using the ladder to climb. How tall is the tallest building that Bob can scale using his ladder? Image source: http://www.inkity.com/shirtdesigner/prints /clipArt1/S7531210.png

5. Solution Bob will be able to reach the maximum possible height when the ladder is as close to the building as possible. Thus, the height will be one leg of a right triangle with hypotenuse 15 and base 8. Using the Pythagorean Theorem: H 2 + 8 2 =15 2 H 2 = 161 H ≈ 12.69

6. Problem 3 What is the length of the hypotenuse of this triangle with legs of length 3x – 2 and 2x + 2 and with hypotenuse of length 3x + 3?

7. Solution The hypotenuse has a length of roughly 19.62. Steps: Begin by forming a relationship between the three sides using the pythagorean theorem. (3x-2) 2 + (2x+2) 2 = (3x+3) 2 Simplify by expanding and combining like terms. 4x 2 – 22x – 1 = 0 Solve for x using the Quadratic Formula. Disregarding the negative result, we see that x is equal to about 5.54, so we can solve for the lengths of the sides by plugging them into the original equations.