Question

In a kite ABCD, AB = AD and CB = CD. If ∠ A = 108° and ∠ C = 36° then the ratio of the area of Δ ABD to the area of Δ CBD can be written in the form a - b tan² 36° / c where a, b and c are relatively prime positive integers. Determine the ordered triple (a, b, c).

Answer 1

Since the triangles ABD and CBD have a common base,

hence the ratio of their areas equals the ratio of their heights. 

Since tan 36° = h/x,  then h = x tan 36°.

|||ly tan 72° =  k/x then k = x tan 72°.

Then ordered triple (a, b, c) is (1,1, 2)