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thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Some trig

In triangle ABC,

and

. Let

be the angle bisector of

.

(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

and find r.

(d) Compute

and

using parts a-c. (Do not use a calculator!)

Thanks

Last edited by thedarktiger (2014-03-31 00:53:34)

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Some trig

hi thedarktiger,

Because of the angle bisector, there are lots of angles of 36 and 72 in this diagram, and hence isosceles triangles.  (See diagram)

So the similar triangles follows quickly and leads to

And putting in the x and y lengths

That leads to a quadratic with only one positive solution for r.

You can then use the cosine rule to get cos36 and cos72.

EDIT:  Don't use the cosine rule as you can split an isosceles down the middle to get a right angle and then use adjacent / hypotenuse, for a much quicker result. 

Bob

Last edited by Bob (2014-03-31 02:37:38)

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thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: Some trig

Thanks!

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Good. You can read.