In an isosceles triangle ABC with base AC = 4, the side is 2√10. Find the tangent of the angle ACB.

From the top B we will construct the height BH.

Since triangle ABC is isosceles, its height BH is also the median and bisector, then AH = CH = AC / 2 = 4/2 = 2 cm.

In a right-angled triangle BCH, according to the Pythagorean theorem, we determine the length of the BH leg.

BH ^ 2 = BC ^ 2 – AC ^ 2 – 40 – 4 = 36.

BH = 6 cm.

In a right-angled triangle, the tangent of an acute angle is the ratio of the length of the opposite leg to the length of the adjacent leg.

tgHCB = BH / CH = 6/2 = 3.

Answer: The tangent of the ACB angle is 3.