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Step 1:: Recall the properties of a right triangle.
where $c$ is the length of the hypotenuse, and $a$ and $b$ are the lengths of the other two sides.
In a right triangle, the Pythagorean theorem states that 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. This can be written as:
Step 2:: In the given triangle, $c = 1$ and $a = 1$.
b^2 = c^2 - a^2
Step 3:: Substitute the given values for $c$ and $a$ into the equation:
b^2 = (13)^2 - (12)^2
Step 4:: Calculate the squares:
b^2 = 169 - 144
Step 5:: Subtract:
b^2 = 25
Step 6:: Find the square root of both sides to solve for $b$:
b = \sqrt{b^2} = \sqrt{25}
Step 7:: Calculate the square root:
b = 5
Final Answer
The value of the variable $b$ is 5.
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