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#1 2014-03-31 00:51:02

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 big_smile

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


Good. You can read.

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#2 2014-03-31 02:34:06

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

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.  smile

Bob

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


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 smile

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#3 2014-04-01 01:04:24

thedarktiger
Member
Registered: 2014-01-10
Posts: 91

Re: Some trig

Thanks!


Good. You can read.

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