Special Right Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The sides are in the ratio 1 : √3 : 2.

Front

What is the rule for a 30-60-90 triangle?

Back

If the shortest side (opposite the 30° angle) is x, then the lengths of the sides are x (shortest), x√3 (opposite the 60° angle), and 2x (hypotenuse).

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The sides are in the ratio 1 : 1 : √2.

Front

What is the rule for a 45-45-90 triangle?

Back

If each leg is x, then the hypotenuse is x√2.

Front

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

Back

In special right triangles, the angles determine the ratios of the lengths of the sides.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the shorter leg?

Back

5 (the shorter leg is half the hypotenuse).

Front

If the shorter leg of a 30-60-90 triangle is 4, what is the length of the longer leg?

Back

4√3 (the longer leg is the shorter leg multiplied by √3).

Front

What type of triangle is formed by angles 30°, 60°, and 90°?

Back

30°-60°-90° triangle.

Front

What type of triangle is formed by angles 45°, 45°, and 90°?

Back

45°-45°-90° triangle.

Front

In a 30-60-90 triangle, if the longer leg is 6√3, what is the hypotenuse?

Back

12 (the hypotenuse is twice the shorter leg, which is 6).