In an isosceles triangle ABC, the side AB is 20 and the base AC is 32. Find tgA.

Let’s draw from the top B in height to the base of the AC, which in the isosceles triangle will also be the median, and therefore AH = CH = AC / 2 = 32/2 = 16 cm.

In a right-angled triangle ABH, we define the leg BH by the Pythagorean theorem.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 400 – 256 = 144.

BH = 12 cm.

Then tgA = BH / AH = 12/16 = 3/4 = 0.75.

Answer: tgA = 0.75.