is trigonometry used in only right angled Triangles if yes then in diagram below its not right angle?? Tan alpha and tan beta

Dear student, No, trigonometry can be used in an triangle other than 90 degree as well. The thing is in school we only apply trigonometry in right angle triangle, in higher classes you will study about the sine rule which is applied to any triangle. Talking about this diagram shown by you, I will suggest that to post the complete question as well so that we an help you more efficiently. Regards