In a triangle ABC AB = BC = 8, angle BAH = 60 degrees. Find the height AH?

The ABC triangle is isosceles, since AB = BC = 8 cm.In an isosceles triangle, the angles at the base are equal, which means:

∠ А = ∠ С = 60 °;

The sum of all the angles of a triangle is always 180 °, we find the angle B:

∠ B = 180 ° – ∠ A – ∠ C = 180 ° – 60 ° – 60 ° = 60 °.

Since all angles in a triangle are the same, it means that the ABC triangle is equilateral (all sides are the same):

AB = BC = AC = 8 cm.

The height in an isosceles triangle is also the median (halves the side), which means:

AH = 1/2 AC = 1/2 * 8 = 4 cm.

Answer: 4 cm