Special Right Triangles 45-45-90 and 30-60-90

What is a 45-45-90 triangle?

• A triangle with angles of 30°, 60°, and 90°.

• A special right triangle where the angles are 45°, 45°, and 90°. The legs are of equal length, and the hypotenuse is √2 times the length of each leg.

• A triangle where all three sides are of equal length.

• A triangle with one angle measuring 90° and the other two angles measuring 45° and 45°.

In a 30-60-90 triangle, if the longer leg is 6√3, what is the length of the hypotenuse?

• 10

• 12

• 14

• 8

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

• If the legs are of length 'a', then the hypotenuse is 'a√2'.

• If the legs are of length 'a', then the hypotenuse is '2a'.

• If the legs are of length 'a', then the hypotenuse is 'a/√2'.

• If the legs are of length 'a', then the hypotenuse is 'a + a'.

What is the value of the hypotenuse in a 45-45-90 triangle with legs of length 1?

• √2

• 1

• 2

• √3

If the legs of a 45-45-90 triangle are 7, what is the hypotenuse?

• 7

• 14

• 7√2

• 49

Find the length of the hypotenuse in a 45-45-90 triangle with legs of length 4.

• 4√2

• 8

• 4

• 2√2

What is the value of x in a 30-60-90 triangle if the hypotenuse is 12?

• 6

• 8

• 10

• 4

What is the formula to find the hypotenuse in a 45-45-90 triangle?

• Hypotenuse = leg × √2

• Hypotenuse = leg × 2

• Hypotenuse = leg × √3

• Hypotenuse = leg + leg

What is a 30-60-90 triangle?

• A triangle with angles of 30°, 60°, and 90° where the side opposite the 30° angle is half the hypotenuse.

• A triangle with angles of 45°, 45°, and 90° where all sides are equal.

• A triangle with angles of 30°, 30°, and 120° where the sides are in a 1:2 ratio.

• A triangle with angles of 60°, 60°, and 60° where all sides are equal.

Find the length of the longer leg in a 30-60-90 triangle if the shorter leg is 5.

• 5√3

• 10

• 5

• 15