Triangle Lengths

Question

Isosceles triangle ABC, with AB=BC, has a height, DB, of 9 inches. Angle A measures 60 degrees. How long is AC?

Answer 1

An isosceles triangle with a 60 degree vertex is equilateral. You can confirm this with the sine law.

If you divide angle A in half, the the new line segment (height) will extend to point D, at the midpoint of BC.

You can calculate the length of side AC with the pythagorean theorem.