Step-by-step explanation:
law of cosine :
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of C.
so, in our case
3² = 3² + 3²×3 - 2×3×3×sqrt(3)×cos(A)
0 = 3²×3 - 18×sqrt(3)×cos(A)
27 = 18×sqrt(3)×cos(A)
cos(A) = 27/(18×sqrt(3)) = 3/(2×sqrt(3)) =
= 0.866025404...
A = 30°
FYI : since it is an isoceles triangle, C = A = 30°.
and therefore B = 180 - 30 - 30 = 120°.
as the sum of all angles in a triangle is always 180°.
