Pythagorean theorem solve for b

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$ \red A^2+ B^2= C^2 \\ \red x^2 + 24^2= {26}^2 $

Step 3

Solve for the unknown.

$ \red x^2 + 24^2= 26^2 \\ \red x^2 + 576= 676 \\ \red x^2 = 676 - 576 \\ \red x^2 = 100 \\ \red x = \sqrt { 100} \\ \red x = 10 $

Problem 1

Find the length of X.

Step 2

Substitute values into the formula (remember 'C' is the hypotenuse).

Remember our steps for how to use this theorem. ?

Let's see if it really works using an example.

Example: A "3, 4, 5" triangle has a right angle in it.


Let's check if the areas are the same:

32 + 42= 52

Calculating this becomes:

9 + 16 = 25

It works ...

  • Engineering & Design: Used for structural analysis, mechanical design, and creating precise technical drawings.

    $ A^2 + B^2 = C^2 \\ 10^2 + \red x^2 = 20^2 $

    Step 3

    Solve for the unknown.

    $ 10^2 + \red x^2 = 20^2 \\ 100 + \red x^2 = 400 \\ \red x^2 = 400 -100 \\ \red x^2 = 300 \\ \red x = \sqrt{300} \approx 17.32 $

    Pythagorean Theorem Calculator for Students


    Free Pythagorean Theorem Calculator for Students

    Our free Pythagorean Theorem Calculator for Students allows you to input the lengths of the legs of any right triangle (sides a and b) and instantly calculate the approximate length of its hypotenuse (side c).

    Simply input values for a and b into the Pythagorean Theorem Calculator, and the value of c will appear in the section directly below.

    The step-by-step solutions help reinforce mathematical concepts.

  • Navigation & Mapping: Forms the basis for calculating the shortest distance between two points in coordinate geometry.

  • Education & Learning: An invaluable tool for students tackling geometry homework. This problems is like example 2 because we are solving for one of the legs.

    This problems is like example 2 because we are solving for one of the legs.

    Step 2

    Substitute values into the formula (remember 'C' is the hypotenuse). From simple geometric demonstrations to complex algebraic proofs, the pythagorean theorem continues to be a cornerstone of mathematical education worldwide.

    Conceptual Animation of Pythagorean Theorem

    Demonstration #1

    More on the Pythagorean theorem

    Demonstration #2

    More on the Pythagorean theorem

    What is the Pythagorean Theorem?

    Video Tutorial

    on How to Use the Pythagorean Theorem

    Step By Step Examples

    of Using the Pythagorean Theorem

    Example 1 (solving for the hypotenuse)

    Use the Pythagorean theorem to determine the length of X.

    Step 1
    The hypotenuse is red in the diagram below:
    Step 2

    Substitute values into the formula (remember 'C' is the hypotenuse).

    • Common Applications & Use Cases

    The pythagorean theorem calculator is essential for:

    • Construction & Building: Quickly calculate diagonal measurements to ensure corners are square, or determine the length of rafters and braces.

    Examples of the Pythagorean Theorem

    When you use the Pythagorean theorem, just remember that the hypotenuse is always 'C' in the formula above.

    pythagorean theorem solve for b

    Our feet & inches mode is perfect for these tasks. Remember that this formula only applies to right triangles.

  • DIY & Home Projects: Ideal for planning layouts, building furniture, or any project that requires perfect right angles. For the purposes of the formula, side $$ \overline{c}$$ is always the hypotenuse.

    This theorem is widely used in mathematics, engineering, construction, navigation, and many other fields where precise distance and angle calculations are required.