In triangle ABC AC = BC, AH is 43 and C is 30 degrees Find AC.

1. According to the condition of the problem AН – the perpendicular dropped from the vertex A of the triangle ABC to the side BC.

We got a triangle ACН, in which the angle CAB is 90 *, according to the condition of the problem, the angle of the BCA is 30 *, and the leg AB is 43.

Hence, the AC side of the ACН triangle can be found as the hypotenuse of a right-angled triangle using trigonometric formulas.

2. Determine the length of the AC side.

AB: AC = sin 30 *;

Find sin 30 * from the table, it is 1/2.

AC = AB: sin 30 * = 43: 1/2 = 43 * 2 = 86.

Answer: The AC side is 86 units.