Mastering Pythagorean Theorem: Right Triangle Problems

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?

• 14 feet

• 10 feet

• 12 feet

• 8 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

• 10 cm

• 14 cm

• 15 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 the base to the top of the park?

• 12.5 meters

• 20 meters

• 18.3 meters

• 15.62 meters

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

• 7 inches

• 7√2 inches

• 14 inches

• 10 inches

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

• 12 cm

• 8 cm

• 6 cm

• 10 cm

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

• 5 feet

• 6 feet

• 7 feet

• 4 feet

A 30-60-90 triangle has a shorter leg measuring 4 inches. What is the length of the longer leg?

• 4√3 inches

• 4 inches

• 2√3 inches

• 8 inches

A kite is flying at a height of 15 meters. If the string makes a 60-degree angle with the ground and the distance from the kite to the point on the ground directly below it is 15 meters, how long is the string?

• 10 meters

• 20 meters

• 10√3 meters

• 15√2 meters

A right triangle has a hypotenuse of 10 meters and one leg measuring 6 meters. What is the length of the other leg?

• 9 meters

• 5 meters

• 8 meters

• 7 meters

A triangular garden has a height of 9 feet and a base of 12 feet. What is the length of the diagonal fence that runs from the base to the top of the garden?

• 9.5 feet

• 8.5 feet

• 10.82 feet

• 12.5 feet