what's the perimeter of this triangle

[mariouzae]

Hi, i have some doubts to find the perimeter of this triangle. a tried a lot of things, but without successful.



thank you very much.

 

[stapel]

Hi, i have some doubts to find the perimeter of this triangle. a tried a lot of things, but without successful.

What are your "doubts"? What have you tried? What did you obtain? On what basis have you decided that you were "unsuccessful"?

Please be complete. Thank you!

Note: Since you are given only two numerical pieces of information, being one side length and one angle measure, it is not possible to "solve" the triangle. You can only find an expression for the perimeter in terms of "3" and the tangent of the one angle.

 

[mmm4444bot]

Mario's diagram shows AB = tg (alpha)

Anybody know what d'heck that means?

tg(alpha) is Portuguese for tan(alpha)

 

[pka]

Hi, i have some doubts to find the perimeter of this triangle. a tried a lot of things, but without successful.

View attachment 3732

thank you very much.

From the given \(\displaystyle \tan (\alpha ) = \dfrac{3}{{\tan (\alpha )}}\), therefore \(\displaystyle \tan (\alpha ) = \sqrt{3}\).

Being a right triangle you know that \(\displaystyle \tan (\alpha ) =m(\overline{BC})^2=3^2+(\sqrt{3})^2\).

Now carry on.