Explanation:
remember : the sum of all angles in a triangle is always 180°.
and remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, c are the sides of the triangle, and A, B, C are the corresponding opposite angles.
in other words, the law of sine enables us to find the length of any side, if we know all angles (we need to know 2 angles, but then we automatically know all 3 angles) and one side.
therefore, we need to begin with the triangle ABC and calculate the length of AC.
once we know that, we can then calculate the length of DC = x in the triangle ACD.
in the triangle ABC we know therefore
AC/sin(80°) = BC/sin(35°) = 8/sin(35°)
AC = 8×sin(80°)/sin(35°) = 13.73567937... cm
and then in the triangle ACD we know
x/sin(75°) = AC/sin(60°)
x = AC×sin(75°)/sin(60°) = 15.32015965... cm
x = AC×sin(75°)/sin(60°) = 15.32015965... cm ≈ 15.3 cm