In triangle ABC, AB = AC, and angle A is equal to 36 degrees. Point D is on AC so that BD bisects angle ABC.
(a) Prove that BC = BD = AD.
(b) Let x = BC and let y = CD. Using similar triangles BCD and ABC, write an equation involving x and y.
(c) Let r = y/x. Write the equation from part (b) in terms of r, and find r.
(d) Find cos 36 degrees and cos 72 degrees using Parts a-c. (Do not use your calculator!)
Thank you so much! Pls include steps :)
You can prove that triangle ABC is a 30-60-90 triangle, with angle A = 30, angle B = 90, and angle C = 60. Then D is the midpoint of AC, so AD = CD = BD. The rest of the parts are easy.
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These have been solved here:
And also, don't try to get people to do the proof for you. You will be in a lot of trouble with the proof part if you are caught.