Special Right Triangles

Front

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

Back

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

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1:√3:2.

Front

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

Back

Multiply the length of the leg by √2 to find the length of the hypotenuse.

Front

If the hypotenuse of a 30-60-90 triangle is known, how can you find the lengths of the other two sides?

Back

The length of the side opposite the 30° angle is half the hypotenuse, and the length of the side opposite the 60° angle is the hypotenuse multiplied by √3/2.

Front

What is the length of the legs in a 45-45-90 triangle if the hypotenuse is 10?

Back

Each leg would be 10/√2, which simplifies to 5√2.

Front

How do you calculate the area of a 30-60-90 triangle?

Back

The area can be calculated using the formula: Area = (1/2) * base * height. For a 30-60-90 triangle, base = x (opposite 30°) and height = x√3 (opposite 60°).

Front

What is the relationship between the angles and sides in special right triangles?

Back

In special right triangles, the angles determine the ratios of the sides, allowing for quick calculations without the need for trigonometric functions.

Front

How can you determine the length of the longer leg in a 30-60-90 triangle if the shorter leg is known?

Back

Multiply the length of the shorter leg (opposite the 30° angle) by √3 to find the length of the longer leg (opposite the 60° angle).

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 other two sides.

Front

If one leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse would be 4√2.