The legs of a right triangle are lengths x and x square root 3. The cosine of the smallest angle of the triangle is _____.

AC=x, BC=x√3, AB is a hypotenuse (look at the pic below)
x√3>x, consequently ∠B<∠A and we have to find cosB, which is (x√3)/AB.
Let's find AB:
AB=√(x²+(x√3)²)=√(x²+3x²)=√(4x²)=2x
Thus, cosB is:
cosB=(x√3)/(2x)=√3/2