4^2 + 5^2 = c^2
The equation 4^2 + 5^2 = c^2 is using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, the two legs have lengths 4 and 5, and we are trying to find the length of the hypotenuse (denoted as c).
Simplifying the equation:
16 + 25 = c^2
41 = c^2
To find the value of c, we take the square root of both sides of the equation:
√41 = √(c^2)
c ≈ √41
So, the approximate value of c is √41.
To find the value of c, let's solve the equation step-by-step:
Step 1: Calculate the powers.
4^2 = 4 x 4 = 16
5^2 = 5 x 5 = 25
Step 2: Add the results.
16 + 25 = 41
Step 3: Take the square root to find c.
√41 ≈ 6.40 (rounded to two decimal places)
Therefore, the value of c is approximately 6.40.
This equation is an example of the Pythagorean theorem, which is a fundamental concept in mathematics. The Pythagorean theorem relates to the sides of a right triangle. In this equation, 4^2 and 5^2 represent the squares of the lengths of the two sides of the right triangle, and c^2 represents the square of the length of the hypotenuse (the side opposite the right angle).
To solve for c, we need to find the square root of the sum of the squares of the two given side lengths. Let's break down the equation and solve it step by step:
Step 1: Calculate the squares of 4 and 5:
4^2 = 4 * 4 = 16
5^2 = 5 * 5 = 25
Step 2: Add the two squares together:
16 + 25 = 41
Step 3: Take the square root of the sum:
√41 ≈ 6.4031 (rounded to four decimal places)
So, the length of the hypotenuse (c) is approximately 6.4031 units.