The area of the ABC triangle is 12 cm2. Find ∠A if AB = 6 cm, AC = 8 cm.

1. To begin with, in the triangle ABC from the vertex B to the base of the AC, we lower the height BH.
2. The area of the triangle ABC = 1/2 * ВН * AC From this formula we find ВН: 12 = 1/2 * ВН * 8 hence ВН = 3
3. Now consider the triangle ABN. It is rectangular because HВ is height (plot).
4. Hypotenuse AB = 6 (given), leg BН, which lies opposite to ∠A, is 3. A leg is equal to half of the hypotenuse if it lies opposite angle = 30 degrees. This means that ∠A = 30 degrees.
Answer: ∠A = 30 degrees.