To solve for [tex]\( a \)[/tex] using the Pythagorean Theorem, we start with the equation given by the theorem:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
We need to isolate [tex]\( a \)[/tex]. To do this, we'll rearrange the equation to solve for [tex]\( a^2 \)[/tex]:
[tex]\[ a^2 = c^2 - b^2 \][/tex]
Now, to find [tex]\( a \)[/tex], we'll take the square root of both sides of the equation:
[tex]\[ a = \sqrt{c^2 - b^2} \][/tex]
Given specific values for [tex]\( b \)[/tex] and [tex]\( c \)[/tex], we can substitute these values into the equation to find the numerical result for [tex]\( a \)[/tex]. In this case, we have:
[tex]\[ b = 0 \][/tex]
[tex]\[ c = 0 \][/tex]
Substituting these values in:
[tex]\[ a^2 = 0^2 - 0^2 \][/tex]
[tex]\[ a^2 = 0 \][/tex]
Taking the square root of both sides:
[tex]\[ a = \sqrt{0} \][/tex]
[tex]\[ a = 0 \][/tex]
Thus, the result for [tex]\( a \)[/tex] is 0. Additionally, the intermediate value for [tex]\( a^2 \)[/tex] would be:
[tex]\[ a^2 = 0 \][/tex]
Hence, the complete solution can be summarized as follows:
[tex]\[ a^2 = 0 \][/tex]
[tex]\[ a = \sqrt{0} = 0 \][/tex]
