Special Right Triangles

Front

What are the properties 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, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

What are the properties 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.

Front

How do you find the length of the hypotenuse in a 30°-60°-90° triangle if the shortest side is known?

Back

If the shortest side (opposite the 30° angle) is known, the hypotenuse can be found by multiplying the shortest side by 2.

Front

How do you find the length of the longer leg in a 30°-60°-90° triangle if the shortest side is known?

Back

The longer leg (opposite the 60° angle) can be found by multiplying the shortest side by √3.

Front

What is the formula to calculate the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

How do you determine the angles in a right triangle?

Back

In a right triangle, the sum of the angles is always 180°. If one angle is 90°, the other two angles must sum to 90°.

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 do you find the length of a side in a 45°-45°-90° triangle if the hypotenuse is known?

Back

If the hypotenuse is known, the length of each leg can be found by dividing the hypotenuse by √2.

Front

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

Back

In special right triangles, specific angle measures correspond to specific side length ratios, allowing for easier calculations.

Front

How can you use special right triangles to solve real-world problems?

Back

Special right triangles can be used in real-world problems involving heights, distances, and angles, allowing for simplified calculations using known ratios.