Real-World Pythagorean Challenges for 8th Graders

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder reaches a height of 8 feet on the wall. Is the ladder the longest side of a right triangle?

• No, the ladder is not part of a triangle.

• The ladder is shorter than the wall.

• The ladder is the shortest side of a triangle.

• Yes, the ladder is the longest side of a right triangle.

A rectangular garden has a length of 10 meters and a width of 24 meters. What is the length of the diagonal that divides the garden into two right triangles?

• 22 meters

• 30 meters

• 26 meters

• 20 meters

A right triangle has one leg measuring 9 cm and the other leg measuring 12 cm. What is the length of the hypotenuse?

• 17 cm

• 15 cm

• 10 cm

• 13 cm

A baseball diamond is a square with each side measuring 90 feet. What is the distance from home plate to second base?

• 90 feet

• 45√2 feet

• 180 feet

• 90√2 feet

A 15-foot tall tree casts a shadow that is 9 feet long. If you draw a right triangle from the top of the tree to the end of the shadow, what is the length of the hypotenuse?

• 15 feet

• 17.49 feet

• 18.5 feet

• 9 feet

A ramp is built to help wheelchair access. If the ramp rises 4 feet over a horizontal distance of 3 feet, what is the length of the ramp?

• 3 feet

• 6 feet

• 5 feet

• 4 feet

A right triangle has a hypotenuse of 13 cm and one leg measuring 5 cm. What is the length of the other leg?

• 8 cm

• 10 cm

• 6 cm

• 12 cm

A swimming pool is rectangular, measuring 30 feet by 40 feet. What is the length of the diagonal across the pool?

• 45 feet

• 50 feet

• 55 feet

• 60 feet

A kite is flying at a height of 20 meters and is 15 meters away from the point directly below it on the ground. How long is the string of the kite?

• 18 meters

• 25 meters

• 22 meters

• 30 meters

A right triangle has angles of 90 degrees, 30 degrees, and 60 degrees. If the side opposite the 30-degree angle is 5 cm, what is the length of the hypotenuse?

• 6 cm

• 12 cm

• 10 cm

• 8 cm