TITLE: Given the base and angles of an isosceles triangle, how to find length of the two sides?
QUESTION [5 upvotes]: I can't seem to find a textbook solution to this. It is always assumed that the length of the sides is know.

Isolceles triangle
So the base $a$ is known. The bottom angles where $\alpha$ and the two sides $b$ touch, are known. 
What is $h$?

REPLY [2 votes]: You can calculate h 
1) using a and b
(a/2) * (a/2) + h * h = b * b
2) using sine law or cosine law http://www.transtutors.com/math-homework-help/laws-of-triangle/
h/ sinα = b / sin 90