Math Is Fun Forum

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Hard Triangle Trig Problem

In triangle GHI, we have GH = HI = 25 and GI = 40. What is \sin\angle GIH?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Hard Triangle Trig Problem

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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.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Hard Triangle Trig Problem

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Hard Triangle Trig Problem

Last edited by thickhead (2016-09-25 20:39:20)

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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.}

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Re: Hard Triangle Trig Problem

Hi thickhead, per your hint I solved the problem and got 3/5 as well. I just built a right triangle by drawing an altitude HM and used  point as the midpoint to apply the pythag thereom then found sin GIH which was just 15/25 (or 3/5)

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Hard Triangle Trig Problem

Imagine

with

being the vertex of the isosceles triangle. If we drop an altitude from

to

, we get two right triangles. Let's call the midpoint

.

and since

, by Pythagorean Theorem,

. So

.

Last edited by evene (2016-09-28 16:03:54)