In triangle abc, angle c is a right angle and bc=5. if measure of angle b = 30 degrees, find ac
a) sqrt3/5
b) 5/2
c) 5sqrt3/2
d) 5sqrt3/3

Answer = d

using the 30 - 60 - 90 triangle theorem

side across from the angle

across from angle 30 is x
across from angle 60 is x rad. 3
across from 90 is 2x

BC is across from angle 60
so BC is the x rad 3
set the given measurement equal to it

x sqrt 3 = 5
÷ sqrt 3 ÷ sqrt 3
x = (5/ sqrt 3)
multiply top and bottom by the radical to get rid of the radical in the bottom

x = (5/ sqrt 3) × (sqrt 3/sqrt 3)
x = 5 sqrt 3/ 3

since side BC is x
BC = 5 sqrt 3/ 3

* Drawing the triangle diagram would help*