Answer:
a = 12 units
Step-by-step explanation:
Equation given is [tex]a^2 + 16^2 = 20^2[/tex]
First we have to evaluate the powers.
[tex]16^{2}[/tex] = [tex]16*16[/tex]=[tex]256[/tex]
[tex]20^{2}[/tex] = [tex]20*20[/tex]=[tex]400[/tex]
So we can now write the equation again as:
[tex]a^2 +256 =400[/tex]
Now we have to undo the addition,
[tex]a^2=400-256 [/tex]
[tex]a^2=144 [/tex]
Now we have to find the square root of [tex]a^2[/tex] to get the value of [tex]a[/tex]
[tex]\sqrt{a^{2}} = \sqrt{144}[/tex]
[tex]a=12[/tex] or [tex]a=-12[/tex]
But the length of a leg cannot be a negative value, so we can take the +12.
a = 12 units
