Question

I don’t know what to do here

Answer 1

The answer is CD = √3

This is because of the fact that a 30-60-90 right triangle has proportions of 1-√3-2 based on the length opposite of the angle. Since we are given the segment opposite to the right angle as 2, we know that we can use the base numbers for the proportions to find the rest. Since CD is opposite of the 60 degree angle, it must be √3.

Answer 2

The ratio of the sides in a 30-60-90 triangle are 1:sqrt3:2    where 1 is shortest leg  and 2 is the hypotenuse  so in the big triangle:-

BC= 2, AB = 4 and AC = 2sqrt3.

 Similarly for triangle CDB  

BC  = 2  therefore  CD = sqrt3 answer