Flashcard: Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios that make calculations easier. The two main types are the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2. The legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

What are the side ratios of a 30-60-90 triangle?

Back

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

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle if one leg is 5?

Back

If one leg is 5, the hypotenuse is 5√2, since the hypotenuse is √2 times the length of each leg.

Front

How do you find the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4?

Back

If the shorter leg is 4, the longer leg is 4√3, since the longer leg is √3 times the length of the shorter leg.

Front

What is the formula to calculate the area of a right triangle?

Back

The area of a right triangle is calculated using the formula: Area = (1/2) × base × height.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

If the legs of a 45-45-90 triangle are each 6, what is the length of the hypotenuse?

Back

The hypotenuse is 6√2, since it is √2 times the length of each leg.

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, since it is half the length of the hypotenuse.

Front

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

Back

In a right triangle, one angle is always 90 degrees, and the sum of the other two angles is always 90 degrees.