Special Right Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles measure 30°, 60°, and 90°. The sides are in the ratio 1:√3:2.

Front

What is a 45°-45°-90° triangle?

Back

A special right triangle where the angles measure 45°, 45°, and 90°. The sides are in the ratio 1:1:√2.

Front

In a 30-60-90 triangle, what is the relationship between the short leg and the long leg?

Back

The long leg is √3 times the length of the short leg.

Front

In a 45°-45°-90° triangle, what is the relationship between the legs and the hypotenuse?

Back

The hypotenuse is √2 times the length of each leg.

Front

What is the formula to find the length of the hypotenuse in a 30-60-90 triangle?

Back

Hypotenuse = 2 × (length of the short leg).

Front

What is the formula to find the length of the long leg in a 30-60-90 triangle?

Back

Long leg = √3 × (length of the short leg).

Front

What is the formula to find the length of the legs in a 45°-45°-90° triangle?

Back

Leg = (length of the hypotenuse) / √2.

Front

If the short leg of a 30-60-90 triangle is 5, what is the length of the hypotenuse?

Back

Hypotenuse = 2 × 5 = 10.

Front

If the hypotenuse of a 45°-45°-90° triangle is 14, what is the length of each leg?

Back

Each leg = 14 / √2 = 7√2.

Front

What is the area of a 30-60-90 triangle with a short leg of 6?

Back

Area = (1/2) × (short leg) × (long leg) = (1/2) × 6 × (6√3) = 18√3.