Special Right Triangles Warm Up

Front

What are the two special right triangles commonly studied in geometry?

Back

The two special right triangles are the 45-45-90 triangle and the 30-60-90 triangle.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

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

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

Front

If the legs of a 45-45-90 triangle are each 8 units long, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 8√2 units.

Front

If the hypotenuse of a 30-60-90 triangle is 10 units, what is the length of the side opposite the 30-degree angle?

Back

The length of the side opposite the 30-degree angle is 5 units.

Front

What is the formula for finding the length of the hypotenuse in a 45-45-90 triangle?

Back

The formula is hypotenuse = leg × √2.

Front

What is the formula for finding the length of the longer leg in a 30-60-90 triangle?

Back

The formula is longer leg = shorter leg × √3.

Front

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

Back

The length of the longer leg is 6√3 units.

Front

What is the area of a 45-45-90 triangle with legs of length 10 units?

Back

The area is (10 × 10) / 2 = 50 square units.

Front

How do you derive the side lengths of a 30-60-90 triangle from the hypotenuse?

Back

The side opposite the 30-degree angle is half the hypotenuse, and the side opposite the 60-degree angle is (hypotenuse × √3) / 2.