Special Right Triangles & Pythagorean Theorem

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The legs are of equal length, and the hypotenuse is √2 times the length of a leg.

Front

What is the relationship between the legs and hypotenuse in a 45-45-90 triangle?

Back

The hypotenuse is equal to the length of a leg multiplied by √2.

Front

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

Back

Divide the length of the hypotenuse by √2.

Front

What is a 30-60-90 triangle?

Back

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

Front

What is the relationship between the sides in a 30-60-90 triangle?

Back

The length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

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

Back

Multiply the length of the shorter leg (opposite the 30° angle) by 2.

Front

What is the Pythagorean Theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Front

How can the Pythagorean Theorem be applied to find missing side lengths?

Back

If two sides of a right triangle are known, the length of the hypotenuse can be found using c = √(a² + b²). Conversely, if the hypotenuse and one leg are known, the other leg can be found using a = √(c² - b²).

Front

What is the value of x in a 45-45-90 triangle with legs of length 4?

Back

x = 4√2.

Front

What is the value of y in a 30-60-90 triangle with a shorter leg of length 4?

Back

y = 4√3.