Remember that
In any triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle
In this problem
the smallest interior angle is 30 degrees
that means
The shortest side is always opposite the smallest interior angle
the shortest side is 1 in ----> opposite to the angle of 30 degrees
see the figure below to better understand the problem
we have
AC= 1 in ------> given
sin(30)=AC/AB -----> by opposite side divided by the hypotenuse in a right triangle
sin(30)=1/2
therefore
1/2=1/AB
AB=2 in
Find out the length BC
Applying the Pythagorean Theorem
AB^2=BC^2+AC^2
substitute given values
2^2=BC^2+1^2
BC^2=4-1
BC=√3 in
