Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

scalene triangle question

Hi, if we have a scalene triangle with : 112,28 and 40 degrees. and that we have a side of lenght 4 between 28 and 40. Can we find the height of the triangle without using the sine law ?

Thank you!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: scalene triangle question

hi Al-Allo

By 'sine law' I'm assuming you mean this:

Certainly that would be a way to get an answer.

Without this you could construct a number of equations using right angled trig. and then try to solve these.  It wouldn't be easy and would still require trig. of some sort.  LATER EDIT.  This method shown below.

There's a formula for calculating area called Heron's formula, that uses all three sides; but, without the sine rule I don't know how you would get these.

Using Sketchpad, I got an answer of 5.21.  LATER EDIT:  See my next post for correction.  You could do this similarly with Geogebra.  But I'm assuming you want an analytical answer.

So my answer to your question is "I know of no such method."  That doesn't mean there isn't one though.  No one can claim that.  There may be a new topic in maths, yet to be discovered, that does what you want.  Maybe you could be its discoverer. 

Bob

Last edited by Bob (2014-08-16 06:51:28)

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: scalene triangle question

Hi;

If I have understood the problem correctly I am getting:

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: scalene triangle question

hi Al-Allo and bobbym,

Thought about it some more and most of post 2 is wrong.  Sorry. 

Firstly, I scaled my Sketchpad diagram up to improve the accuracy, but completely forgot to scale it back for my 'answer'.

So my revised answer is 5.21/4 = 1.3

But I'm finding a different height as this diagram (not accurate) shows.

Now, assuming you'll allow 'ordinary' trig:

So substituting for y

and substituting for x

Bob

ps.  Or simplify equations 1 and 2 to

Last edited by Bob (2014-08-16 06:55:50)

---

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: scalene triangle question

Hi Bob;

It looks like that depending on how you orient the triangle you will come up with 3 different heights. Is there any reason to support which side is the base from the wording of the problem?

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: scalene triangle question

hi bobbym,

It is yet another example of a loosely worded question.  I seem to have had several recently.

I imagined drawing this triangle (with ruler and protractor).  I'd start with base = 4; then make the angles 28 and 40; then find the vertex 'at the top'.  So, in my head, the height was 'up' from the 4. 

But, that's just my interpretation.  Who knows ? Maybe I should start a campaign :CABWE, the Campaign Against Badly Worded Exercises.

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