Finding the Distance of a Line Using the Pythagorean Theorem

What is the formula for finding the hypotenuse?

• a²⁺b²=c²

• a-b=c

• a+b=c

• c-a=c

Solve for x

(hint: use the Pythagorean Theorem)

• 22

• 9.38

• 4

• 88

The map to the right shows 2 different routes Ms. Bentsen can take to drive to the airport from her house. How many miles could Ms. Bentsen save by traveling on Airport Road instead of Mountain Highway and Oak Road to get to the airport? (hint: Use the Pythagorean Theorem)

• 20 miles

• 30 miles

• 35 miles

• 60 miles

A 10-foot ladder is leaning against the wall. The bottom of the ladder is 4 feet from the base of the wall. Which of the following is closest to the distance from the top of the ladder to the base of the wall? (use Pythagorean Theorem)

• 9 ft

• 6 ft

• 11 ft

• 14 ft

A piece of paper that Brittany has is 11 inches tall and 8.5 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

• 7.5 in

• 12.4 in

• 13.9 in

• 14.3 in

The Pythagorean Theorem ONLY works on which triangle?

• Obtuse

• Acute

• Equilateral

• Right

An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30^o angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?

• 50 ft

• 43 ft

• 87 ft

• 25 ft

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance (perimeter) traveled?

• 17 miles

• 37 miles

• 32 miles

• 40 miles

A person is flying a kite using 40 meters of kite string as shown in the diagram. What is the approximate measure of the height, h, of the kite?

• 80 m

• 20 m

• 34.64 m

• 28.28 m

Nick and Tyler left the library and biked home. Nick biked 1,931 meters due north on Pine Street to his home. Tyler biked 3,380 meters due west on Elm Street. Then, Tyler decided to go to Nick’s house by taking Main Street. What is the distance to the nearest meter that Tyler traveled on Main Street to go to Nick’s house?

• 1,449 meters

• 2,774 meters

• 3,893 meters

• 5,311 meters