Answer:
[tex]a=9[/tex]
Step-by-step explanation:
In this problem, you can use the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) to find what a is. The steps are shown below:
Steps (variables a, b, and c are in italics):
-You can rearrange the formula from the Pythagorean Theorem, which is[tex]a^{2} +b^{2} =c^{2}[/tex] to only get a because we want to know what a is.
Rearranged: [tex]a=\sqrt{c^{2}-b^{2} }[/tex] or [tex]a=-\sqrt{c^{2}-b^{2} }[/tex] It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.
-Since we know what c and b are, you can plug them into the new formula:
[tex]a=\sqrt{15^{2}-12^{2} }[/tex]
-Simplify it:
[tex]a=\sqrt{225-144}[/tex]
-Subtract inside the radical:
[tex]a=\sqrt{81}[/tex] Then simplify it to get [tex]a=9[/tex].
You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2} =c^{2}[/tex]):
Steps
-Plug a, b, and c into the formula [tex]a^{2} +b^{2} =c^{2}[/tex]:
[tex](9)^{2} +(12)^{2} =(15)^{2}[/tex]
-Simplify to get:
[tex]81+144=225[/tex]
-Add:
[tex]225=225[/tex] This is very true. So our answer is correct.
ANSWER: [tex]a=9[/tex]
Sorry for the long explanation, but I hope you understand and that this helps with your question! :)
