Special Right Triangles

Front

What are the properties 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 the longest side.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by 2.

Front

How do you find the length of the longer leg in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by √3.

Front

What are the properties of a 45-45-90 triangle?

Back

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

Front

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

Back

Divide the length of the hypotenuse by √2.

Front

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

Back

Multiply the length of the leg by √2.

Front

What is the relationship between the angles and sides in a right triangle?

Back

In a right triangle, the side opposite the largest angle (90 degrees) is the hypotenuse, and the other two sides are the legs.

Front

What is the formula for the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the legs.

Front

How can you determine the length of a side in a right triangle using trigonometric ratios?

Back

You can use sine, cosine, and tangent ratios to find the lengths of the sides based on the angles.

Front

What is the sine ratio in a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.