Trigonometry ( high school level )

1. Nov 7, 2012

sambarbarian

Cot A + Cot B + Cot C = under root 3

ABC is which type of triangle ?

1) isosceles
2) equilateral
3) right angled
4) none of these

2. Nov 7, 2012

SammyS

Staff Emeritus
What have you tried?

Where are you stuck?

There are indications in some of your previous posts that you know that you are expected to show an attempt at a solution.

3. Nov 7, 2012

sambarbarian

that is the problem , i can't even begin to solve this . i don't know how to start this one .

P.S - i did think of option c) because the function cot would require a 90 degree angle .

4. Nov 7, 2012

Mentallic

What do you mean cot requires a 90o angle? Can you draw the graph of cot? Specifically for the values of x between 0o and 180o (because a triangle can only have these angles obviously).

5. Nov 7, 2012

sambarbarian

yes i can , as i said i don't know where to begin so i just wrote whatever came to my mind .

6. Nov 7, 2012

SammyS

Staff Emeritus
Here's a very basic place to start.

A + B + C =  ?

7. Nov 7, 2012

180 degree

8. Nov 7, 2012

SammyS

Staff Emeritus
Solve for C.

Then see if you can take it a step or two further on your own & let us know what you come up with.

Last edited: Nov 7, 2012
9. Nov 7, 2012

G.I.

Ok, I suggest you to try. Start with the simpliest solution: the equilateral one. You know the angles, does the equation work?

In a second time you can try with right angled one.
You know the first angle (say A) is 90° and the sum of the three angles have to be 180°, right? So, posing the unknown angle as B, the angle C is fixed.
I don't know what do you mean with high scool level (I'm from an other country), but if you know trigonometric formulas (for sin and cos of sum and difference of angles) you can easily manipulate the cot and find a quadratic equation you can try to solve. (I hope I make myself clear)

In a third time you can try to solve the isosceles one. Is a bit more difficult than above, but you can do it: Isosceles means 2 angles are the same, say A = B. Now, C have to be 180-(A+B) = 180 -(2*A). Same of second solution, manipulate using trigonometric formulas and you have a quadratic equation.

Now have just to try. I know that find the angules isn't required, but I'm not sure that the quadratic equations have solution (I have no time to solve them).

(I apologize for any possible mistakes, I'm trying to improve my English.)

10. Nov 7, 2012

sambarbarian

Thanks G.I , i got it