How to solve pietagorous terum

Mathematics

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Answer

The Pythagorean theorem 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 (legs).

Step-by-step solution

6 steps

The formula is:

a2+b2=c2a^2 + b^2 = c^2

Where:

  • aa and bb are the lengths of the two legs of the right-angled triangle.
  • cc is the length of the hypotenuse.

To solve for a missing side:

  1. Identify the hypotenuse (cc) and the two legs (aa and bb).

    The hypotenuse is always the longest side and is opposite the right angle.

  2. Substitute the known values into the formula a2+b2=c2a^2 + b^2 = c^2.

  3. Solve for the unknown side.

    *   If you are solving for the hypotenuse ($c$), calculate $a^2 + b^2$ and then take the square root of the result: $c = \sqrt{a^2 + b^2}$.
*   If you are solving for a leg (e.g., $a$), rearrange the formula: $a^2 = c^2 - b^2$, and then take the square root: $a = \sqrt{c^2 - b^2}$.

    Example: If a right triangle has legs of length 3 units and 4 units, what is the length of the hypotenuse?

  4. a=3a = 3, b=4b = 4.

    We need to find cc.

  5. Substitute into the formula

    32+42=c23^2 + 4^2 = c^2.

  6. Calculate

    9+16=c29 + 16 = c^2.

    25=c225 = c^2 c=25c = \sqrt{25} c=5c = 5

    The hypotenuse is 5 units long.

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