8-3 Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The sides opposite the 45° angles 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 side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

If the legs of a 45-45-90 triangle are each 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

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

Back

Hypotenuse = leg × √2.

Front

If the hypotenuse of a 45-45-90 triangle is 8√2, what is the length of each leg?

Back

Each leg is 8.

Front

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

Back

The longer leg is 5√3.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 6?

Back

The hypotenuse is 12.

Front

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

Back

The shorter leg is 5.

Front

What is the area of a 45-45-90 triangle with legs of length 4?

Back

Area = (1/2) × leg × leg = (1/2) × 4 × 4 = 8.

Front

What is the perimeter of a 30-60-90 triangle with a shorter leg of 3?

Back

Perimeter = shorter leg + longer leg + hypotenuse = 3 + 3√3 + 6.