Trigonometry ( high school level )

[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

 

[SammyS]

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

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.

 

[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 .

 

[Mentallic]

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 .

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

 

[sambarbarian]

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

 

[SammyS]

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 .

Here's a very basic place to start.

A + B + C =  ? 

 

[sambarbarian]

180 degree

 

[SammyS]

180 degree

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.

 

[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.)

 

[sambarbarian]

Thanks G.I , i got it