Answer:
[tex]\boxed {\boxed {\sf b= \sqrt{192}}}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use Pythagorean Theorem to find the sides.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
In this triangle, 8 and x are the legs because they form the right angle. 16 is the hypotenuse because it is opposite the right angle.
[tex]a=8 \\c=16[/tex]
Substitute the values into the formula.
[tex]8^2+b^2=16^2[/tex]
Solve the exponents.
- 8² = 8*8= 64
- 16²=16*16=256
[tex]64+b^2=256[/tex]
Subtract 64 from both sides to isolate the variable.
[tex]64-64+b^2= 256-64 \\b^2=192[/tex]
Take the square root of both sides.
[tex]\sqrt {b^2}=\sqrt{192}\\ b=\sqrt{192}[/tex]
The missing side is equal to √192
