Exploring Right Triangles: Properties and Ratios Quiz

A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and the base of the ladder is 6 feet from the wall, how high up the wall does the ladder reach?

• 10 feet

• 6 feet

• 4 feet

• 8 feet

A 45-45-90 triangle has legs of length 8 cm. What is the length of the hypotenuse?

• 8√2 cm

• 4√2 cm

• 8 cm

• 16 cm

A triangular park has a right angle at one corner. If one leg measures 12 meters and the other leg measures 16 meters, what is the length of the hypotenuse?

• 22 meters

• 20 meters

• 24 meters

• 18 meters

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

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

• Longer leg: 10 inches, Hypotenuse: 5 inches

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

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

A right triangle has one angle measuring 30 degrees. If the hypotenuse is 14 meters, what is the length of the side opposite the 30-degree angle?

• 12 meters

• 10 meters

• 7 meters

• 5 meters

A triangular roof has a height of 9 feet and a base of 12 feet. If the roof forms a right triangle, what is the length of the roof's slope?

• 15 feet

• 8.5 feet

• 10.82 feet

• 12 feet

In a right triangle, one leg is 7 cm long and the other leg is 24 cm long. What is the length of the hypotenuse?

• 25 cm

• 15 cm

• 20 cm

• 30 cm

A 45-45-90 triangle is inscribed in a square. If the side length of the square is 10 cm, what is the length of each leg of the triangle?

• 7 cm

• 5√2 cm

• 5 cm

• 10 cm

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

• 10 cm

• 14 cm

• 8 cm

• 12 cm

A 30-60-90 triangle has a hypotenuse of 20 meters. What are the lengths of the shorter leg and the longer leg?

• Shorter leg: 5 meters, Longer leg: 10 meters

• Shorter leg: 10 meters, Longer leg: 17.32 meters

• Shorter leg: 8 meters, Longer leg: 15 meters

• Shorter leg: 12 meters, Longer leg: 17 meters