Question

Can someone explain geometric relationships? Such as Pythagorean theorem ?

Answer 1

so the triangle has 3 sides, keeping in mind that the longest side is always the hypotenuse "c".

so the sides' lengths are 8, 10 and 15, so the legs are 8 and 10, the hypotenuse is 15 hmmmm, well, from the pythagorean theorem, c² = a² + b², meaning the square of the hypotenuse has to equal the sum of the square of the other two, let's see if that's true.

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2+b^2) \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{8}\\ b=\stackrel{opposite}{10}\\ \end{cases} \\\\\\ c=√(8^2+10^2)\implies c=√(64+100)\implies c=√(164) \\\\\\ c\approx 12.81\qquad \qquad \stackrel{\textit{nope, no dice, is not a right-triangle}}{c\\e 15}`