Pythagorean Theorem/Special Right Triangles

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). Formula: a² + b² = c².

Front

What are the side lengths 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. The side opposite the 30° angle is the shortest (1), the side opposite the 60° angle is √3, and the hypotenuse is 2.

Front

What are the side lengths of a 45°-45°-90° triangle?

Back

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

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to solve for the missing side.

Front

What type of angle do the legs of a right triangle form?

Back

The legs of a right triangle form a right angle (90°).

Front

If one leg of a 30°-60°-90° triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 10, since it is twice the length of the shorter leg (5).

Front

If the hypotenuse of a 45°-45°-90° triangle is 10, what is the length of each leg?

Back

Each leg is 10/√2 or 5√2.

Front

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

Back

The sum of the angles in any triangle is 180°. In a right triangle, one angle is 90°, so the other two angles must sum to 90°.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What is the value of x in a 30°-60°-90° triangle if the shorter leg is 5?

Back

x (the longer leg) is 5√3.