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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 :)

 Oct 8, 2020
 #1
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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.

 Oct 8, 2020
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How did you prove that? Also, I would like help for the whole thing, as I am really confused.

Noori  Oct 8, 2020
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And how can triangle ABC be a 30-60-90 triangle when angle A is 36 degrees?

Noori  Oct 8, 2020
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Enjoying week 24 of Int to Geo?

 

These have been solved here:

 

http://www.mathisfunforum.com/viewtopic.php?pid=413642

 

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.

 Oct 8, 2020
edited by Nacirema  Oct 8, 2020

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