In triangle ABC, the height CH is 4, AC = BC, tg A = 0.5. Find AB.

1.Consider triangle AHC.

The tangent of angle A is equal to the ratio of the opposite leg to the adjacent leg, in this case

tgA = CH / CA = 0.5 hence CA is 2 times more than CH, i.e. CA = 2 * CH = 2 * 4 = 8 cm.

2. Consider triangle ABC.

S (ABC) = (AC * BC) / 2 = (AB * CH) / 2, therefore (8 * 8) / 2 = (AB * 4) / 2, multiply both sides of the equation by 2, we get 4 * AB = 64, AB = 64: 4 = 16 (cm).