To solve for [tex]\( a \)[/tex] using the Pythagorean Theorem, follow these steps:
1. Start with the equation provided by the Pythagorean Theorem:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
2. Substitute the given values [tex]\( b = 9 \)[/tex] and [tex]\( c = 12 \)[/tex] into the equation:
[tex]\[ a^2 + 9^2 = 12^2 \][/tex]
3. Calculate [tex]\( 9^2 \)[/tex]:
[tex]\[ 9^2 = 81 \][/tex]
4. Substitute [tex]\( 81 \)[/tex] back into the equation:
[tex]\[ a^2 + 81 = 144 \][/tex]
5. Subtract [tex]\( 81 \)[/tex] from both sides of the equation to isolate [tex]\( a^2 \)[/tex]:
[tex]\[ a^2 = 144 - 81 \][/tex]
6. Perform the subtraction:
[tex]\[ a^2 = 63 \][/tex]
7. To find [tex]\( a \)[/tex], take the square root of both sides of the equation:
[tex]\[ a = \sqrt{63} \][/tex]
8. Calculate the value of [tex]\( \sqrt{63} \)[/tex]:
[tex]\[ a = 7.937253933193772 \][/tex]
So, the value of [tex]\( a \)[/tex] is approximately [tex]\( 7.937 \)[/tex].
