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dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Cosine

In triangle $ABC$, $\angle A = 36^\circ$ and $\angle B = \angle C = 72^\circ$. Let $\overline{BD}$ 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 $r=\frac yx$ and find $r.$

(d) Compute $\cos 36^\circ$ and $\cos 72^\circ$ using Parts a-c. (Do not use your calculator!)

I was able to do a-c.  Can I help on d?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Cosine

hint: Use cosine rule for the angles in

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Cosine

hi dazzle1230

This problem has been asked before here:

http://www.mathisfunforum.com/viewtopic … 83#p365383

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Cosine

I got that

and

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Cosine

Well done!

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob