Answer:
b = [tex]2\sqrt{5}[/tex] = 4.47
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^{2}+b^{2} = c^{2}[/tex]
Let's say a= 2, b= x, and c = 4
Since we need to find the value of x, we will rearrange our equation
[tex]a^{2} + c^{2} = b^{2}[/tex]
Now, we substitute plug in the numbers for the values
[tex](2)^{2} + (4)^{2} = b^{2}[/tex]
Then, find [tex](2)^{2}[/tex] and [tex](4)^{2}[/tex]
[tex](2)^{2} = 4[/tex]
[tex](4)^{2} = 16[/tex]
4 + 16 = [tex]b^{2}[/tex]
Add 4 and 16
4 + 16 = 20
20 = [tex]b^{2}[/tex]
We still need to find what b is by itself, we need to get rid of the exponent.
So, we need to take the square root of both sides.
[tex]\sqrt{20} = \sqrt{b}[/tex]
[tex]\sqrt{20} = 2\sqrt{5}[/tex]
b = [tex]2\sqrt{5}[/tex] = 4.47
And that would be your answer
