In an isosceles triangle ABC AC = BC. Find AC if the height is CH = 12, AB = 10.

Given:

Triangle ABC, AC = BC, CH-height, CH = 12, AB-base, AB = 10

Find: AC

Decision:

1) because. ABC is an isosceles triangle, then CH is both the height and the median, therefore, AH = HB = 5.

2) because. triangle ACH is right-angled, then according to t. Pythagoras:

AC ^ 2 = AH ^ 2 + CH ^ 2

AC ^ 2 = 5 ^ 2 + 12 ^ 2

AC ^ 2 = 25 + 144

AC ^ 2 = 169

AC = 13

Answer: AC = 13