Question

Please help, this is due today!

Answer 1

`x=√(28)`

Explanation:

See attachment for annotation and further explanation!! (Please let me know if it needs clarifying)

To begin to find x, we can see that we have a triangle (in blue in attachment). To find x, we need to find the 3rd side length, can use reverse pythagorean theorem to find x.

But, to find the 3rd side length, we can use the parallel line (in yellow) as the 3rd side length. To find the 3rd side length, we can use pythagorean theorem with another triangle (in green).

Pythagorean theorem is as follows:

`a^2+b^2=c^2`

Substitute in the green triangle values:

`6^2+6^2=c^2`

`36+36=c^2\\72=c^2\\c=8.48 or √(72)`

Now that we have the 3rd side for the blue triangle, we can use pythagorean theorem again to solve for x:

`a^2+b^2=c^2`

`√(72)^2+b^2=10^2`

square root and square cancel out

`72+b^2=100`

subtract 72 from both sides

`b^2=28\\b=√(28)`

So,
`x=√(28)`

Hope this helps! :)