In the figure below angle B is a right angle mBAC 30 degree

In the figure below, angle B| is a right angle, m(BAC) = 30 degree | and the length of AC = 12| If CD = 5|, find the length of AD| 2 squareroot 229| 229| 6| squareroot 229| 458| None of the above.

Solution

from the diagram

cos(m(BAC)) =AB/AC

cos(30^o) =AB/12

AB=12cos(30^o)

AB=12(³/2)

AB=63

sin(m(BAC)) =BC/AC

sin(30^o) =BC/12

BC=12sin(30^o)

BC=12(¹/2)

BC=6

BD=BC+CD

BD=6+5

BD=11

from right angled triangle

AD²=AB²+BD²

AD²=(63)²+11²

AD²=108+121

AD²=229

AD=(229)