Pythagorean Thm & 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 ratios in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratios of the lengths of the sides are 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 ratios in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the ratios of the lengths of the sides are 1 : 1 : √2. The two legs are equal in length (1), and the hypotenuse is √2 times the length of each leg.

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

If one leg of a 30-60-90 triangle is 7, how do you find the length of the hypotenuse?

Back

In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg. Therefore, the hypotenuse is 7 * 2 = 14.

Front

What is the height of an equilateral triangle with side length s?

Back

The height (h) of an equilateral triangle can be found using the formula h = (√3/2) * s.

Front

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

Back

In a 30-60-90 triangle, the longer leg is √3 times the length of the shorter leg. If the shorter leg is x, then the longer leg is x√3.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If the hypotenuse of a right triangle is 10 and one leg is 6, how do you find the other leg?

Back

Use the Pythagorean Theorem: b = √(c² - a²). Here, b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the formula to find the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula A = (1/2) * base * height.