Exploring Special Right Triangles and Their Properties

A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and reaches 8 feet up the wall, how far is the base of the ladder from the wall?

• 8 feet

• 6 feet

• 10 feet

• 4 feet

A 45-45-90 triangle has legs of length x. If the perimeter of the triangle is 20 units, what is the value of x?

• 10(2 - √2)

• 5

• 10

• 15

A triangular park has a right angle at one corner. If one leg measures 6 meters and the other leg measures 8 meters, what is the length of the hypotenuse?

• 10 meters

• 14 meters

• 12 meters

• 8 meters

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

• Long leg: 10 cm, Hypotenuse: 5√3 cm

• Long leg: 10√3 cm, Hypotenuse: 5 cm

• Long leg: 5√3 cm, Hypotenuse: 10 cm

• Long leg: 5 cm, Hypotenuse: 5√2 cm

A right triangle has one angle measuring 30 degrees. If the hypotenuse is 12 inches long, what is the length of the side opposite the 30-degree angle?

• 4 inches

• 8 inches

• 10 inches

• 6 inches

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

• 10.82 feet

• 12 feet

• 11 feet

• 8.5 feet

In a right triangle, if one leg is 7 cm and the hypotenuse is 25 cm, what is the length of the other leg?

• 24 cm

• 30 cm

• 15 cm

• 20 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?

• 14 cm

• 10 cm

• 8 cm

• 12 cm

A 30-60-90 triangle has a hypotenuse of 16 inches. What are the lengths of the other two sides?

• Shorter leg: 10 inches, Longer leg: 12 inches

• Shorter leg: 6 inches, Longer leg: 9 inches

• Shorter leg: 8 inches, Longer leg: 8√3 inches (approximately 13.86 inches)

• Shorter leg: 5 inches, Longer leg: 15 inches