Special Right Triangles Quiz

What are the missing side lengths if you are working with a 30-60-90 triangle. The short side is 6 feet.

• Longer leg: 8 feet, Hypotenuse: 10 feet
• Longer leg: 12 feet, Hypotenuse: 15 feet
• Longer leg: 5 feet, Hypotenuse: 9 feet
• Longer leg: 6√3 feet, Hypotenuse: 12 feet

Answer explanation

The hypotenuse is twice as long as the short leg. The long leg is the short leg multiplied by the square root of 3.

In a 30-60-90 triangle, if the hypotenuse is 10 feet, what are the lengths of the other sides?

• Shorter leg: 8 feet, Longer leg: 8√3 feet

• Shorter leg: 5√3 feet, Longer leg: 5 feet

• Shorter leg: 6 feet, Longer leg: 6√3 feet

• Shorter leg: 5 feet, Longer leg: 5√3 feet

What is the length of the hypotenuse in a 30-60-90 triangle if the longer leg is 9√3 feet?

• 9√3 feet

• 9√2 feet

• 18 feet

• 9 feet

If the longer leg of a 30-60-90 triangle is 15 feet, what is the length of the shorter leg?

• 5 feet

• 5√3 feet

• 10 feet

• 15√3 feet

What is the length of the hypotenuse if the leg is 5 feet for a 45-45-90 triangle?

• 5 feet
• 5√2 feet
• 10 feet
• 7 feet

What is the length of a leg for a 45-45-90 triangle if the hypotenuse is 10 feet?

• 7 feet
• 10 feet
• 5√2 feet
• 6 feet

Answer explanation

To find the length of a leg, give the hypotenuse, of a 45-45-90 triangle you must divide by the square root of 2. You do not leave a radical in the denominator. So you must multiply the numerator and denominator by the square root of 2.

What is the hypotenuse if a leg is 20 feet square root of 2 for a 45-45-90 triangle?

• 30 feet

• 50 feet

• 40 feet

• 20 feet

In a 45-45-90 triangle, if one leg is 8 feet, what is the length of the hypotenuse?

• 8 feet

• 16 feet

• 8√2 feet

• 4√2 feet

What is the length of the longer leg in a 30-60-90 triangle if the hypotenuse is 14 feet?

• 7 feet

• 7√3 feet

• 14 feet

• 14√3 feet

If the shorter leg of a 30-60-90 triangle is 10 feet, what is the length of the hypotenuse?

• 10 feet

• 15 feet

• 20 feet

• 10√3 feet