Enter the lengths of two sides into the calculator to determine the length of the hypotenuse.
3 4 5 Rule Formula
The following formula is used to calculate the length of the sides in a right-angled triangle using the 3 4 5 rule.
a² + b² = c²
Variables:
- a is the length of one side (units)
- b is the length of the other side (units)
- c is the length of the hypotenuse (units)
To calculate the length of the sides using the 3 4 5 rule, square the length of one side (a), square the length of the other side (b), and add these two values together. The result should be equal to the square of the length of the hypotenuse (c). If the lengths of the sides are in the ratio 3:4:5, a right angle is formed between sides a and b.
What is a 3 4 5 Rule?
The 3 4 5 rule is a mathematical principle used in construction and carpentry to create right angles. It is based on the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. By measuring 3 units along one side, 4 units along the other, and ensuring the diagonal between these two points measures 5 units, a right angle is formed.
How to Calculate 3 4 5 Rule?
The following steps outline how to use the 3 4 5 Rule to calculate the length of the hypotenuse in a right triangle.
- First, determine the lengths of the two sides of the right triangle (a and b) in the given units.
- Next, use the 3 4 5 Rule to check if the lengths of the two sides satisfy the rule. The rule states that if the lengths of the two sides are in the ratio of 3:4, then the triangle is a right triangle.
- If the lengths of the two sides satisfy the 3 4 5 Rule, then the triangle is a right triangle.
- Finally, use the formula a² + b² = c² to calculate the length of the hypotenuse (c).
Example Problem:
Use the following variables as an example problem to test your knowledge.
a = 3 units
b = 4 units
Using the 3 4 5 Rule, we can determine that the lengths of the two sides satisfy the rule, indicating that the triangle is a right triangle.
Now, we can use the formula a² + b² = c² to calculate the length of the hypotenuse (c).
Substituting the given values:
3² + 4² = c²
9 + 16 = c²
25 = c²
Taking the square root of both sides:
c = 5 units
Therefore, the length of the hypotenuse (c) in the right triangle is 5 units.
