Problem 3 Finding Distance

Dog Agility Dog agility courses often contain a seesaw obstacle, as shown below. To the nearest inch, how far above the ground are the dog's paws when the seesaw is parallel to the ground?

a 2 + b 2 = c 2 Pythagorean Theorem 26 2 + b 2 = 36 2 Substitute . 676 + b 2 = 1296 Simplify . b 2 = 620 Subtract  676  from each side . b ≈ 24.8997992 Use a calculator to take the positive square root . table with 5 rows and 3 columns , row1 column 1 , eh squared , plus , b squared , column 2 equals , c squared , column 3 cap pythagoreancap theorem , row2 column 1 , 26 squared , plus , b squared , column 2 equals , 36 squared , column 3 cap substitute . . , row3 column 1 , 676 plus , b squared , column 2 equals , 1296 , column 3 cap simplify , . , row4 column 1 , b squared , column 2 equals 620 , column 3 cap subtract . 676 . fromeachside . . , row5 column 1 , b , column 2 almost equal to . 24.8997992 , column 3 cap useacalculatortotakethepositivesquareroot . . , end table

The dog's paws are 25 in. above the ground.

✓ Got It?

3. The size of a computer monitor is the length of its diagonal. You want to buy a 19-in. monitor that has a height of 11 in. What is the width of the monitor? Round to the nearest tenth of an inch.

Take Note Theorem 8-2: Converse of the Pythagorean Theorem

Theorem

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

If …

a 2 + b 2 = c 2 eh squared , plus , b squared , equals , c squared

Then …

Δ A B C cap delta eh b c is a right triangle

You will prove Theorem 8-2 in Exercise 52.