Power triangle represents the active power, reactive power and apparent power of AC circuit in aright angle triangle. The three sides of the right angle triangle shows the relationship between all three powers. The power triangle is a useful tool for calculating the power active, reactive and apparent power in a AC circuit if two out of three power is known. There are many combinations of electrical load like pure resistive, inductive capacitive or combination of RL,RC,RLC,LC etc. The inductive, and capacitive load draws a reactive power from the source and feed back the power to source again.
From above phasor diagram, it is clear that inductive and capacitive circuit draw reactive current. The total current in the circuit is thus the vector sum of active current and reactive current. We can show the active,reactive and apparent power by a right angle triangle.
The reactive component draws a reactive current and its magnitude is ISinɸ. The active component draws active current, and its magnitude is I Cosɸ. The Product of the reactive component of current ( ISinɸ) and voltage(V) is the reactive power. The Product of the active component of current ( I Cosɸ), and voltage(V) is the active power. Resultant vector sum of the active and reactive power is the apparent power.
What is a Power Triangle?
Hypotenuse = Apparent Power
Active Power (P) = VI Cosɸ [ Cosɸ = Power Factor ] 
Reactive Power (Q) = VI Sinɸ 
Apparent Power(S ) = VI^{*} 
We can find the power of the AC circuit by power triangle, if two out of three powers is available. Then , all three powers can be drawn on power triangle to show the relationship between the active power, reactive power and apparent power.
Summary

We denote the active power on the base of power triangle. The watt meter measures the active power. The active power is the useful power used by the equipment to do useful work. The examples of the equipment drawing are electrical motor, oven, heater,geyser etc.

The reactive power (inductive type) is used for electrical machines’ functioning. The induction motor draws inductive reactive power to produce rotating magnetic field. Similarly, transformer also draw reactive power to set up magnetic flux in its core. The reactive power is necessary evils. Without consuming reactive power, an electrical machine can not work. The cause of poor power factor is drawing of more reactive power from the supply source.
 To improve the power factor of the system, we add capacitor banks to nullify the effect of inductive reactive power. The capacitor banks draws reactive power in just phase opposition of the inductive reactive power, and thus the net reactive power of the circuit decrease.

The apparent power shows the total circuit current whether its is active or reactive. There is endeavors to reduce the apparent power for economic operation of the electrical network. The less the reactive power, the less is the losses in the transmission line.

After determining the active power and reactive power, the Power factor can be calculated using the power triangle.
Power Triangle Example No. 1
A wound coil that has an inductance of 150mH and a
resistance of 25 Ω is connected to a 110V 50Hz supply.
Calculate:
a) the impedance of the coil, b) the current,c) the power factor,and d) the apparent power consumed.
Also draw the resulting power triangle for the above coil.
R = 25 Ω
Z = √ ( R^{2} + X_{L}^{2}) = √ ( 25^{2} + 47.1^{2}) = 53.32 Ω
^{The impedance of the coil is Z = 53.32 Ω}
Cosɸ = R/Z = 25/53.32 = 0.46
ɸ = Cos^{1} (0.46) = 62.61°
Sinɸ = √ ( 1 – Cos^{2}ɸ) = √ ( 1 – 0.46^{2}) = 0.88
Reactive Power = VI Sinɸ = 110 x 2.06 x 0.88 = 199.40 VAr
Apparent Power = √ ( Active Power^{2} + Reactive Power^{2} )
= √ ( 104.23^{2} + 199.40^{2} ) =224.99 VA