Math Is Fun Forum

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

try this tri

Interior angles of a triangle are 120, 40 and 20 degrees. The longest side is 10 cm longer than the shortest side. Woops! sorry, I forgot to add that I'm to find the perimeter of the triangle. It was almost 1am when I posted this.

To start, would I make up a value for the longest side and add 10? I can use cosine law and or sine law. I know that the longest side is opposite the largest angle. Shortest side is opposite shortest angle.

Last edited by reallylongnickname (2011-05-08 06:07:23)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: try this tri

Hi reallylongnickname;

Is this what you are thinking of? Now what do you need?

---

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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: try this tri

Hi reallylongnickname,

There are no solutions for such a triangle!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: try this tri

hi all

Wooah,

There are no solutions for such a triangle!

Are you sure?

I have AC = 16.53333   and BC = 6.53333

(EDIT improved accuracy in my next post)

see diagram

Bob

ps got to do some gardening .... back with a method shortly

Last edited by Bob (2011-05-08 05:39:11)

---

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: try this tri

Hi bob,

Yes, my cosine rule is wrong!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: try this tri

hi gAr

I thought as follows:

Draw any triangle with those angles (they add to 180 so this is always possible).

Measure AC and BC and work out AC - BC  = k say.

Apply the (multiplicative) scale factor 10/k to all sides.

Now AC - BC = 10/k . (k) = 10.

Now to work out a solution (I'm not claiming my earlier values as I did that using Sketchpad (ie. measuring).

I'll use bobbym's suggestion for the sides.

sine rule (x + 10)/sin120 = x/sin20

rearranging

x = 10 sin20 /(sin120-sin20) =  6.527036

Bob

Last edited by Bob (2011-05-08 05:46:32)

---

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

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: try this tri

I have AC = 16.53333   and BC = 6.53333

Woops! sorry, I forgot to add that I'm to find the perimeter of the triangle. It was almost 1am when I posted the original Q.
Thx Bob and all others. I assume AC is the longest and BC the shortest side. I then used the sin formula to find the 3rd side AB. Then added all three to equal 35.2 The answer for the perimeter agrees with answer in text book of 35cm.

Last edited by reallylongnickname (2011-05-08 06:36:35)

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: try this tri

Hi bob,

Okay.
Meanwhile, I was working for a general solution, trying cosine rule itself.

*removed a wrong conclusion!*

Last edited by gAr (2011-05-09 02:03:52)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: try this tri

x = 10 sin20 /(sin120-sin20) =  6.527036

Bob

Could u brk this down plz. I don't know how this rearrangment came about.

Last edited by reallylongnickname (2011-05-08 11:10:42)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: try this tri

hi reallylongnickname

Ok.  Call the longest side x + 10, and the shortest x.

You are right that the longest side is opposite the largest angle, and the smallest side is opposite the smallest angle.

So, by 'sine rule'

'cross multiply'

'multiply out'

'bring the x term to the RHS

'factorise the x'

'divide by the bracket'

I agree with your value for AB and for the perimeter.

Hope that helps,

Bob

ps.  If 'x' is not the shortest side you will get a different solution.

When you can,  use the sine rule rather than the cosine rule because there are less calculations / chances for errors.

Last edited by Bob (2011-05-08 21:39:27)

---

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: try this tri

Hi

Sorry, forgot about the other two angles.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."