Special Right Triangles and Trig Ratios

Front

What is a special right triangle?

Back

A special right triangle is a triangle with specific angle measures that allow for easy calculation of side lengths. 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 lengths of the legs are equal, and the length of 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 lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle, √3 is opposite the 60-degree angle, and 2 is the hypotenuse.

Front

What is the tangent ratio?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Front

What is the sine ratio?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Front

What is the cosine ratio?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Front

How do you find the length of a side using the tangent ratio?

Back

To find the length of a side using the tangent ratio, use the formula: tan(angle) = opposite/adjacent. Rearrange to solve for the unknown side.

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): a² + b² = c².

Front

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

Back

The hypotenuse is 4√2.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the side opposite the 30-degree angle?

Back

The length of the side opposite the 30-degree angle is 5.