Mastering Right Triangles and the Pythagorean Theorem

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 positioned correctly according to the Pythagorean theorem?

• Yes, but it should be longer.

• Yes, the ladder is positioned correctly.

• No, the ladder is leaning too far away.

• No, the ladder is too short.

A triangular park has sides measuring 5 meters, 12 meters, and 13 meters. Can you determine if this park is a right triangle?

• No, the park is a scalene triangle.

• No, the park is an obtuse triangle.

• Yes, the park is an equilateral triangle.

• Yes, the park is a right triangle.

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

• 15 cm

• 17 cm

• 13 cm

• 10 cm

A rectangular garden has a diagonal that measures 10 meters. If one side of the garden is 6 meters, what is the length of the other side?

• 9 meters

• 8 meters

• 5 meters

• 7 meters

A right triangle has legs measuring 7 inches and 24 inches. Calculate the length of the hypotenuse and verify if it forms a right triangle using the Pythagorean theorem.

• 25 inches

• 26 inches

• 20 inches

• 30 inches

A ramp is built to help wheelchair access. If the ramp is 4 feet high and 3 feet long, is it a right triangle?

• Yes, it is a right triangle.

• Yes, it is a square.

• No, it is an obtuse triangle.

• No, it is a trapezoid.

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

• 12 cm

• 10 cm

• 8 cm

• 14 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

• 180 feet

• 90√2 feet

• 90 feet

A right triangle has a hypotenuse of 10 meters and one leg of 6 meters. Can you find the length of the other leg and confirm if it is a right triangle?

• 5 meters

• 8 meters

• 7 meters

• 9 meters

A 5-foot tall person is standing 12 feet away from a wall. If they look up at a 45-degree angle, how high on the wall will they be looking?

• 10 feet

• 12 feet

• 15 feet

• 17 feet