In triangle ABC AC = BC, CH height is 16, cos A = 0.6. Find AC.

1. Consider a triangle ABC – isosceles, therefore AC = BC. The height also divides the base into two equal parts.

2. Consider a triangle AНС – rectangular, cos A = 0.6.

3. We can use the formula:
sin ^ 2 a = 1 – 0.6 ^ 2;
sin a = 0.64;
sin a = 0.8.

4. I remembered the formula sin a = CH / AC.

5. Find the speaker.
AC = CH / sin a;
AC = 16 / 0.8;
AC = 20.

Answer: AC = 20.