Mastering Ratios in Special Right Triangles

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?

• 8 feet

• 6 feet

• 10 feet

• 4 feet

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

• 8√2 inches

• 4√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: 5√3 cm, Hypotenuse: 10 cm

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

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

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

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

• 15 cm

• 8 cm

• 10 cm

A ramp is built to help wheelchair access. If the ramp is 4 feet long and rises to a height of 3 feet, what is the horizontal distance from the base of the ramp to the wall?

• 4.5 feet

• 2.65 feet

• 1.5 feet

• 3.5 feet

In a right triangle, if the hypotenuse is 15 cm and one leg is 9 cm, what is the length of the other leg?

• 12 cm

• 8 cm

• 10 cm

• 14 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 the hypotenuse of the triangle?

• 10 cm

• 5√2 cm

• 10√2 cm

• 15 cm

A right triangle has one angle measuring 30 degrees. If the hypotenuse is 20 meters, what is the length of the side opposite the 30-degree angle?

• 25 meters

• 10 meters

• 5 meters

• 15 meters

A triangular roof has a height of 6 feet and a base of 8 feet. If the roof forms a right triangle, what is the length of the roof's slope?

• 5 feet

• 10 feet

• 8√2 feet

• 2√13 feet