In triangle ABC, angle A = 36 and angle B = angle C = 72. Let line BD be the angle bisector of angle ABC.

In triangle ABC, angle A = 36 and angle B = angle C = 72. Let line BD be the angle bisector of angle ABC.

 

(a) Prove that BC = BD = AD.

 

(b) Let x = BC and let y = CD. Using similar triangles ABC and BCD, write an equation relating x and y.

 

(c) Write the equation from Part b in terms of r = y/x and find r. 

 

(d) Compute cos 36 and cos 72 using Parts a-c and without using a calculator.

 

Thanks!