Question

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

Answer 1

Explanation:

`BD=√(10^2-2^2)\\ BD=√(100-4) \\BD=√(96)\\ BD=4√(6)`

Similar triangles

`tan(\alpha )=tan(\alpha )\\\\ \\(BC)/(BA) =(BD)/(AD) \\\\(BC)/(10) =(4√(6) )/(2)\\\\BC=2√(6) *10\\BC=20√(6)`

Pythagorean theorem

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