Real-World Pythagorean Challenges for Right Triangles

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 correct length according to the Pythagorean theorem?

• The ladder is 8 feet long according to the Pythagorean theorem.

• The ladder is 12 feet long according to the Pythagorean theorem.

• Yes, the ladder is 10 feet long according to the Pythagorean theorem.

• The ladder is 14 feet long according to the Pythagorean theorem.

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?

• 20 meters

• 30 meters

• 22 meters

• 26 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

• 13 cm

• 15 cm

• 10 cm

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

• 45√2 feet

• 90√2 feet

• 180 feet

• 90 feet

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

• 9 feet

• 20 feet

• 17.44 feet

• 15 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?

• 5 feet

• 6 feet

• 3 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?

• 10 cm

• 12 cm

• 15 cm

• 8 cm

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

• 60 feet

• 55 feet

• 45 feet

• 50 feet

A kite is flying at a height of 50 meters. If the string of the kite is 70 meters long, how far is the kite from the point directly below it on the ground?

• 70 meters

• 20 * sqrt(6) meters (approximately 48.99 meters)

• 50 meters

• 30 meters

A right triangle has angles of 90 degrees, 45 degrees, and 45 degrees. If one leg measures 7 cm, what is the length of the hypotenuse?

• 10.5 cm

• 8.5 cm

• 7.5 cm

• 9.9 cm