Would be great if this could be answered by tomorrow!

Question

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971

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+1450

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!

Guest · Answer 1 · 2019-11-20T02:05:45

(b) x^3 - 3*x^2*y + y^3 = 0.

(c) r^3 - 3r + 1 = 0.

(d) cos 36 = (-1 + sqrt(3))/2, cos 72 = (-1 - sqrt(3))/2.