Right triangles are one of the fundamental shapes in geometry. They have unique properties that make them useful in various applications. One common task is to find the lengths of the legs of a right triangle when only the hypotenuse and one leg are known. In this blog post, we will discuss the steps involved in finding the missing leg of a right triangle.

Step 1: Understanding the Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). The formula can be written as:

c2 = a2 + b2

where c represents the length of the hypotenuse, and a and b represent the lengths of the legs.

Step 2: Gathering the known information

Before we can find the missing leg, we need to identify what information we already have. Typically, we know the length of the hypotenuse and the length of one leg. Let’s say the length of the known leg is ‘a’, and the length of the hypotenuse is ‘c’.

Step 3: Applying the Pythagorean theorem

Using the Pythagorean theorem formula, we can rearrange it to solve for the missing leg, ‘b’. The equation becomes:

b = √(c2 – a2)

Here, we subtract the square of the known leg from the square of the hypotenuse and take the square root of the result to find the length of the missing leg.

Step 4: Perform the calculation

Now that we have the equation, simply substitute the known values into the formula and solve for ‘b’. Calculate the difference between the square of the hypotenuse and the square of the known leg, and then determine the square root of that difference. The result will be the length of the missing leg.

Step 5: Check your answer

It is always good practice to verify your answer. Once you have found the length of the missing leg, you can plug it back into the Pythagorean theorem equation to ensure that both sides of the equation are equal.

By using the Pythagorean theorem and following the steps outlined above, you can find the lengths of the legs in a right triangle when the hypotenuse and one leg are known. Remember to double-check your calculations and ensure your answer satisfies the equation. Understanding the principles behind right triangles and the Pythagorean theorem is useful in geometry and applicable to various fields where triangles are involved.

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