I am having problems understanding how to
solve problems like the following:
a2 + b2 = c2
Please help me where I can understand solving problems such as the one above.
Do you mean ??
A squared + B squared = C squared??
Let's take a right angle triangle with the two short sides (adjacent to the right angle) that measure 4 inches and 5 inches.
A^2 = 4 squared = 16
B^2 = 5 squared = 25
16 + 25 = C^2
41 = C^2
6.4 = C
dunno
Learn not cheat!
To solve a problem like the one you provided, which involves the sum of two squares, we need to understand a concept called the Pythagorean theorem. The 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 other two sides.
Let's break down the problem step by step:
1. Identify the values of a and b: In the equation a^2 + b^2 = c^2, a and b represent the lengths of the two sides of a right triangle. These sides are usually referred to as the "legs" of the triangle.
2. Determine the value of c: The variable c represents the length of the hypotenuse. It is the longest side of a right triangle. In the equation, c^2 represents the square of that length.
3. Apply the Pythagorean theorem: By substituting the values of a and b into the equation a^2 + b^2 = c^2, you can solve for c. Square the values of a and b, then add them together, and finally take the square root of the sum to find the length of c.
For example, let's say you are given that a = 3 and b = 4. To solve for c, substitute these values into the equation:
(3^2) + (4^2) = c^2
9 + 16 = c^2
25 = c^2
Now, take the square root of both sides:
√25 = √c^2
5 = c
Therefore, in this example, when a = 3 and b = 4, the length of the hypotenuse (c) is 5.
Remember, the Pythagorean theorem is specifically used for right triangles. If you have a different type of triangle, this equation would not be applicable.