Exploring Triangle Ratios: Special Right Triangles 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?

• 6 feet

• 4 feet

• 8 feet

• 10 feet

A 45-45-90 triangle has legs of equal length. If one leg measures 8 inches, what is the length of the hypotenuse?

• 4√2 inches

• 8√2 inches

• 16 inches

• 8 inches

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?

• 18 meters

• 22 meters

• 24 meters

• 20 meters

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

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

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

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

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

A right triangle is formed by a ramp leading to a loading dock. If the ramp is 15 feet long and the height of the dock is 9 feet, how far is the base of the ramp from the wall?

• 12 feet

• 16 feet

• 14 feet

• 10 feet

In a right triangle, if one angle measures 30 degrees and the hypotenuse is 20 meters, what is the length of the side opposite the 30-degree angle?

• 5 meters

• 10 meters

• 25 meters

• 15 meters

A triangular garden is designed in the shape of a 45-45-90 triangle. If the area of the garden is 32 square feet, what is the length of each leg?

• 6 feet

• 8 feet

• 10 feet

• 12 feet

A right triangle has one leg measuring 7 cm and a hypotenuse measuring 25 cm. What is the length of the other leg?

• 24 cm

• 15 cm

• 10 cm

• 20 cm

A 30-60-90 triangle has a hypotenuse of 18 inches. What are the lengths of the shorter leg and the longer leg?

• Shorter leg: 9 inches, Longer leg: 9√3 inches (approximately 15.59 inches)

• Shorter leg: 8 inches, Longer leg: 14 inches

• Shorter leg: 10 inches, Longer leg: 15 inches

• Shorter leg: 6 inches, Longer leg: 12 inches

A right triangle is formed by a kite flying at a height of 30 feet, with a horizontal distance of 40 feet from the observer. How long is the string of the kite?

• 40 feet

• 60 feet

• 50 feet

• 30 feet