45-45-90 and 30-60-90 Special Triangle Shortcuts

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. The lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the 90-degree angle.

Front

If each leg of a 45-45-90 triangle is 5 units, what is the length of the hypotenuse?

Back

5√2 units.

Front

What is the formula to find the hypotenuse of a 30-60-90 triangle if the shorter leg is known?

Back

Hypotenuse = 2 * (shorter leg).

Front

If the shorter leg of a 30-60-90 triangle is 6 units, what is the length of the longer leg?

Back

6√3 units.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the longer leg is 12 units?

Back

The hypotenuse is 24 units.

Front

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

Back

Leg = hypotenuse / √2.

Front

If the hypotenuse of a 45-45-90 triangle is 10√2 units, what is the length of each leg?

Back

10 units.

Front

What is the value of a leg in a 30-60-90 triangle if the hypotenuse is 18 units?

Back

The shorter leg is 9 units, and the longer leg is 9√3 units.

Front

What is the area of a 45-45-90 triangle with legs of length 5 units?

Back

Area = (1/2) * leg * leg = (1/2) * 5 * 5 = 12.5 square units.