Special Triangles

Front

What is a special triangle?

Back

A special triangle is a triangle with specific properties that make calculations easier, such as the 30-60-90 triangle and the 45-45-90 triangle.

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, where 1 is the length of the side opposite the 30° angle, √3 is opposite the 60° angle, and 2 is the hypotenuse.

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, where the legs are equal and the hypotenuse is √2 times the length of each leg.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

To find the hypotenuse in a 30-60-90 triangle, multiply the length of the shorter leg (opposite the 30° angle) by 2.

Front

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

Back

To find the longer leg in a 30-60-90 triangle, multiply the length of the shorter leg (opposite the 30° angle) by √3.

Front

How do you find the length of the legs in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if you know the length of the hypotenuse, divide it by √2 to find the length of each leg.

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

How can you use the Pythagorean theorem with special triangles?

Back

You can use the Pythagorean theorem to verify the side lengths of special triangles or to find missing side lengths when the triangle is not in its special form.

Front

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

Back

In special triangles, the angles determine the ratios of the sides, allowing for quick calculations without needing to use trigonometric functions.

Front

What is the significance of simplifying radicals in triangle problems?

Back

Simplifying radicals helps in expressing side lengths in their simplest form, making it easier to understand and compare lengths.