Answer: [tex]a=\sqrt{c^2-4}[/tex]
Step-by-step explanation:
You know that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
Where "a" and "b" are the legs and "c" is the hypotenuse.
Then, since you need to find the length of side "a" in terms of the hypotenuse "c", you need to solve for "a":
Subtract b² from both sides of the equation:
[tex]a^2+b^2-b^2=c^2-b^2[/tex]
[tex]a^2=c^2-b^2[/tex]
And finally, you need to apply square root to both sides of the equation:
[tex]\sqrt{a^2}=\sqrt{c^2-b^2}\\\\a=\sqrt{c^2-b^2}[/tex]
Then:
[tex]a=\sqrt{c^2-2^2}\\\\a=\sqrt{c^2-4}[/tex]
Answer:
Final answer is [tex]a=\sqrt{c^2-4}[/tex].
Step-by-step explanation:
Given that b=2. Now using Pythagorean theorem, we need to find the value of a in terms of c.
So let's plug b=2 into formula :
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+2^2=c^2[/tex]
[tex]a^2+4=c^2[/tex]
[tex]a^2=c^2-4[/tex]
Take square root of both sides and use principle root as side length can't be negative.
[tex]a=\sqrt{c^2-4}[/tex]
Hence final answer is [tex]a=\sqrt{c^2-4}[/tex].
