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). It can be expressed as: c² = a² + b².

Front

In a 30-60-90 triangle, what is the ratio of the lengths of the sides?

Back

The ratio of the lengths of the sides in a 30-60-90 triangle is 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

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

Back

To find the length of the hypotenuse in a right triangle, 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

What is the length of the short leg in a 30-60-90 triangle if the long leg is 7?

Back

To find the short leg, divide the long leg by √3. Therefore, the short leg is 7/√3.

Front

What is the length of the hypotenuse in a right triangle with legs measuring 4 feet and 3 feet?

Back

Using the Pythagorean Theorem: c = √(4² + 3²) = √(16 + 9) = √25 = 5 feet.

Front

In a 45-45-90 triangle, what is the relationship between the legs and the hypotenuse?

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

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

Back

The hypotenuse is 10√2, since it is √2 times the length of each leg.

Front

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

Back

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

Front

How do you find the length of the longer leg in a 30-60-90 triangle if the short leg is 5?

Back

To find the longer leg, multiply the short leg by √3. Therefore, the longer leg is 5√3.

Front

What is the value of x in a right triangle if the angles are 30°, 60°, and 90°?

Back

The value of x can be determined based on the properties of the triangle. If x is the angle opposite the short leg, then x = 30°.