Solving Special Right Triangles: 45-45-90 and 30-60-90 Examples

What is the hypotenuse of a 45-45-90 triangle if one leg is 8?

• 8√3

• 4√2

• 8√2

• 16

What is the relationship between the sides of a 45-45-90 triangle?

• Hypotenuse is twice as long as a leg

• One leg is √2 times longer than the other

• Legs are congruent; hypotenuse is leg times 2

• Legs are congruent; hypotenuse is leg times √2

How do you find a leg in a 45-45-90 triangle if the hypotenuse is given as 4√2?

• Multiply by 2

• Divide by √2

• Divide by 2

• Multiply by √2

In a 45-45-90 triangle, if the hypotenuse is 8√3, what is one leg?

• 8/√3

• 4√3

• 8

• 4√6

In a 30-60-90 triangle, what is the longer leg if the shorter leg is 4?

• 4√2

• 8

• 2√3

• 4√3

How do you find the hypotenuse in a 30-60-90 triangle if the shorter leg is given?

• Divide the shorter leg by 2

• Multiply the shorter leg by √3

• Multiply the shorter leg by √2

• Multiply the shorter leg by 2

In a 30-60-90 triangle, how is the longer leg related to the shorter leg?

• It is half as long

• It is twice as long

• It is √3 times the shorter leg

• It is √2 times the shorter leg

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

• 5√3

• 5

• 10/√3

• 10√3

What is the length of the longer leg in a 30-60-90 triangle if the hypotenuse is 16?

• 16√3

• 16/√3

• 8√3

• 8

Why does the hypotenuse of a 45-45-90 triangle have a length of x√2 when the legs are of length x?

• Because of the Pythagorean theorem

• Due to the triangle's angles

• It's a property of all triangles

• Because the legs are perpendicular