Answer: 6.6
Step-by-step explanation:
We have two triangles. Find the hypothenuse of the first triangle to make it easier to solve the second triangle.
First triangle:
a = 6
b = 8
c = ?
Use pythagorean's theorem
[tex]c^2=a^2+b^2\\c=\sqrt{a^2+b^2}[/tex]
[tex]c=\sqrt{(6)^2+(8)^2}\\ c=\sqrt{36+64}\\ c=\sqrt{100}\\ c=10[/tex]
This hypothenuse is valid for both triangles. Having said this, we already have 2 sides of the second triangle; c and a. We need to find b.
[tex]c^2=a^2+b^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}[/tex]
[tex]b=\sqrt{(12)^2-(10)^2}\\ b=\sqrt{144-100}\\ b=\sqrt{44}\\ b=6.6[/tex]
