Question

Please help me with this, urgent! Tysm!

Answer 1

Check the picture below.

so due to the purple vertical angles, the triangles are similar triangles, so let's use proportions to get AC.

$\cfrac{3}{5}~~ = ~~\cfrac{x}{6-x}\implies 18-3x = 5x\implies 18=8x\implies \cfrac{18}{8}=x\implies \boxed{\cfrac{9}{4}=x} \\\\[-0.35em] ~\dotfill\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{3}\\ \end{cases}$

$y=\sqrt{x^2+3^2}\implies y=\sqrt{\cfrac{9^2}{4^2}+9}\implies y=\sqrt{\cfrac{81}{16}+9}\implies y=\sqrt{\cfrac{81+144}{16}} \\\\\\ y=\sqrt{\cfrac{225}{16}}\implies y=\sqrt{\cfrac{15^2}{4^2}}\implies y=\cfrac{15}{4}\implies \blacksquare~~ \stackrel{AC}{y}=3\frac{3}{4} ~~\blacksquare$