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

asked Jun 10, 2020 94.5k views

5 votes

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6 votes

Answer:

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

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

Naqeeb answered Jun 16, 2020

5.9k points

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