Pythagorean Problem Solving: Right Triangle Challenges

A ladder is leaning against a wall. If the base of the ladder is 6 feet from the wall and the ladder is 10 feet long, how high up the wall does the ladder reach?

• 8 feet

• 4 feet

• 10 feet

• 6 feet

A right triangle has one leg that measures 8 cm and a hypotenuse that measures 10 cm. What is the length of the other leg?

• 9 cm

• 6 cm

• 5 cm

• 7 cm

A triangular park has a height of 12 meters and a base of 16 meters. If the park is shaped like a right triangle, what is the length of the hypotenuse?

• 22 meters

• 20 meters

• 15 meters

• 18 meters

A 45-45-90 triangle has legs that each measure 5 inches. What is the length of the hypotenuse?

• 7 inches

• 5√2 inches

• 10 inches

• 5 inches

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?

• 6 feet

• 5 feet

• 7 feet

• 4 feet

A right triangle has one leg measuring 7 meters and a hypotenuse measuring 25 meters. Find the length of the other leg.

• 24 meters

• 15 meters

• 20 meters

• 30 meters

A 30-60-90 triangle has a shorter leg of 4 cm. What is the length of the longer leg and the hypotenuse?

• Longer leg: 4√3 cm, Hypotenuse: 8 cm

• Longer leg: 8 cm, Hypotenuse: 12 cm

• Longer leg: 4 cm, Hypotenuse: 4√2 cm

• Longer leg: 6 cm, Hypotenuse: 10 cm

A kite is flying at a height of 30 feet. If the string makes a 60-degree angle with the ground, how far is the kite from the person holding the string?

• 15 feet

• 20√3 feet

• 25 feet

• 30√2 feet

A right triangle has a base of 9 inches and a height of 12 inches. What is the length of the hypotenuse?

• 10 inches

• 15 inches

• 18 inches

• 13 inches

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

• 26 feet

• 22 feet

• 30 feet

• 20 feet