Given that CD = 2 in the following triangle, find the length of side AB. Show all of your calculations and leave your answer in simplified radical form.

Question

Given that CD = 2 in the following triangle, find the length of side AB. Show all of your calculations and leave your answer in simplified radical form.

Answer 1

AB = 8/sqr3 = about 4.62

AC =4, the hypotenuse of a right triangle with sides 2 and 2sqr3

AC^2 = (2sqr3)^2 + 2^2 = 12+4 =16

AC =sqr16 = 4

CB = 4/sq3 = height CD 2 times 2/sqr3 = 4/sqr3

AB^2 =AC^2 + CB^2 = 4^2 + (4/sqr3)^2 = 16 + 16/3 = 64/3

AB =sqr64/3 =8/sqr3 = about 4.62

AB = about 4.62

or in exact radical form

AB = 8/sqr3 = (8/3)sqr3