Question

What is the length of side CD? (the answer is 48 but idk how to get there)

Answer 1

Answer:

Step-by-step explanation:

$BD=\sqrt{10^2-2^2}\\ BD=\sqrt{100-4} \\BD=\sqrt{96}\\ BD=4\sqrt{6}$

Similar triangles

$tan(\alpha )=tan(\alpha )\\\\ \\\frac{BC}{BA} =\frac{BD}{AD} \\\\\frac{BC}{10} =\frac{4\sqrt{6} }{2}\\\\BC=2\sqrt{6} *10\\BC=20\sqrt{6}$

Pythagorean theorem

$CD=\sqrt{BC^2-BD^2} \\CD=\sqrt{(20\sqrt{6} )^2-(4\sqrt{6} )^2} \\CD=\sqrt{400(6)-16(6)} \\CD=\sqrt{2304} \\CD=48$