Hint: Construct the angle bisector of one of the base angles. Thus the 36-72-72 triangle is divded into two triangles, one with angles 36-72-72 and the other 36-36-108.

Now the small triangle is similar to the large one. Therefore




This is the statement of the equivalence of the ratios of length of corresponding sides of the similar triangles. It is also the definition of the Golden Ratio:

When a line segment is divided into two parts of length of a and b such that the ratio of the whole to the longest part is equal to the ratio of the length of the longest part to the length of the shortest, the common ratio is the Golden Ratio.



Solve for