Mastering Special Triangles: Side Length Calculations

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

• 4 feet

• 10 feet

• 6 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

• 8 inches

• 4√2 inches

• 16 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

• 20 meters

• 24 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 cm, Hypotenuse: 5√3 cm

• Longer leg: 10 cm, Hypotenuse: 5 cm

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

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

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?

• 7 meters

• 12 meters

• 10 meters

• 5 meters

A roof is designed in the shape of a right triangle. If the height of the roof is 9 feet and the base is 12 feet, what is the length of the roof's slope?

• 15 feet

• 18 feet

• 12 feet

• 10 feet

In a right triangle, one leg measures 7 cm and the hypotenuse measures 25 cm. What is the length of the other leg?

• 15 cm

• 30 cm

• 24 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?

• 5 cm

• 5√2 cm

• 7 cm

• 10 cm

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

• 12 inches

• 8 inches

• 6 inches

• 10 inches

A triangular garden is designed with a right angle. If the two legs measure 9 feet and 12 feet, what is the area of the garden?

• 72 square feet

• 36 square feet

• 54 square feet

• 45 square feet