If DB = 2...?

Question

If DB = 2, find CB, AB, AD, CD, and AC.
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thank you! please explain!

Answer 1

Please remember the very useful and important fact that the hypotenuse of a 30-60-90 right triangle is twice as long as the shortest leg. Also, in any of such triangle, the other leg is sqrt(3) as long as the shortest leg.
Therefore, if DB = 2
BC = 4, since DBC is a 30-60-90 right triangle and BC the hypotenuse;
AB = 8, since ABC is a 30-60-90 right triangle and AB the hypotenuse;
CD = 2*sqrt(3), since CD is "the other leg" in triangle DBC;
AC = 4*sqrt(3), since AC is "the other leg" in triangle ABC;
AD = CD*sqrt(3) = 6; since AD is "the other leg" in triangle ADC; by the way, AD can also be calculated from AD*DB=CD^2, thus AD = CD^2/DB = 6