Integer triangle not) satisfy formula_151. We can generate the full equivalence class of similar triangles that satisfy B=3A by using the formulas where formula_28 and formula_27 are integers such that formula_157. Note that all triangles with B = 3A (whether with integer sides or not) satisfy formula_158. The only integer triangle with three rational angles (rational numbers of degrees, or equivalently rational fractions of a full turn) is the equilateral triangle. This is because integer sides imply three rational cosines by the law of cosines, and by Niven's theorem a rational cosine coincides with a rational angle if and only if the
Velocity triangle Velocity triangle In turbomachinery, a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the working fluid in a turbomachine. Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine. The vector nature of velocity is utilized in the triangles, and the most basic form of a velocity triangle consists of the tangential velocity, the absolute velocity and the relative velocity of the fluid making up three sides of the triangle. A general velocity triangle consists of the following vectors: The following angles are encountered during the analysis: