Pythagorean Theorem: Missing Side

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

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

What is the formula to find a missing side when the hypotenuse and one side are known?

Back

If the hypotenuse (c) and one side (a) are known, the missing side (b) can be found using the formula: b = √(c² - a²).

Front

What is the relationship between the sides 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-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

What is the relationship between the sides 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 can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side. If a² + b² = c², then the triangle is a right triangle.

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to calculate distances and angles.

Front

How do you solve for a missing side when given the lengths of the other two sides?

Back

Use the Pythagorean Theorem: If you know the lengths of sides a and b, you can find the hypotenuse c using c = √(a² + b²), or find a missing side using a = √(c² - b²) or b = √(c² - a²).

Front

What is the first step in solving a Pythagorean Theorem problem?

Back

Identify which sides of the triangle are known and which side is missing. Label the sides as a, b, and c (where c is the hypotenuse).

Front

What is the value of the hypotenuse if one side is 3 and the other side is 4?

Back

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