Find the indicated angle or side Give an exact answer Find t

Find the indicated angle or side. Give an exact answer. Find the exact length of side a. squareroot 109 squareroot 47 9 7

Solution

apply cosine law:

cos30 = (b^2 + c^2 - a^2)/2bc

b = 2 ; c= 5sqrt3

sqrt3/2 = (4 + 75 - a^2)/2*5sqrt3*2

79 - a^2 = 20*3/2

79 - a^2 = 30

a^2 = 49

a = 7