Pythagorean Challenges: Right Triangles in Real Life

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. How long is the ladder?

• 8 feet

• 5 feet

• 12 feet

• 10 feet

A right triangle has one leg that measures 5 cm and the other leg that measures 12 cm. What is the length of the hypotenuse?

• 13 cm

• 15 cm

• 14 cm

• 10 cm

A triangular park has a height of 10 meters and a base of 24 meters. What is the length of the diagonal path that runs from one corner of the park to the opposite corner?

• 15.62 meters

• 18.3 meters

• 12.5 meters

• 20 meters

A 45-45-90 triangle has legs that each measure 7 inches. What is the length of the hypotenuse?

• 7√2 inches

• 10 inches

• 7 inches

• 14 inches

A kite is flying at a height of 30 meters. If the string makes a 60-degree angle with the ground, how far is the kite from the point directly below it on the ground?

• 20√3 meters

• 15 meters

• 10√3 meters

• 25 meters

A right triangle has one leg measuring 9 feet and a hypotenuse measuring 15 feet. What is the length of the other leg?

• 14 feet

• 12 feet

• 8 feet

• 10 feet

A 30-60-90 triangle has a shorter leg of 5 inches. What is the length of the longer leg and the hypotenuse?

• Longer leg: 10 inches, Hypotenuse: 5 inches

• Longer leg: 5 inches, Hypotenuse: 5√3 inches

• Longer leg: 5√3 inches, Hypotenuse: 10 inches

• Longer leg: 10√3 inches, Hypotenuse: 5√2 inches

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?

• 6 feet

• 4 feet

• 3 feet

• 5 feet

A right triangle has a base of 8 meters and a height of 15 meters. What is the length of the hypotenuse?

• 20 meters

• 10 meters

• 12 meters

• 17 meters

A triangular garden has a height of 12 feet and a base of 16 feet. What is the length of the diagonal fence that runs from one corner of the garden to the opposite corner?

• 20 feet

• 18 feet

• 14.42 feet

• 10 feet