Finding the Directionality of a Sound

I recently performed a noise lab and I am required to write a program to find the room constant of the room where the data was collected. Basically I would be using the formula:

Lp = Lw + 10log(Q/[4*pi*r^2] + 4/R)

Where Lp is the sound pressure level which was collected during the experiment, Lw was given by the professor, Q is 1 and r is the distance from the sound source to the reciever. My problem is that the Lw given is in 4 different directions - it's hard to explain but the sound source is a rectangular box, and the source was emitted in a north, west, east, south way. But my receiver was always on an angle and I can't figure out how to calculate a resultant sound, because sound isn't a force so I can't just sum them together. There's a picture attached showing what I mean. The four arrows are the sounds being emitted. Is there some way I can calculate the directionality to get the sound that the receiver picked up?

I found this equation for a directionality index,

DI = Lp(theta) - Lp

Could this be used?

Thanks for looking! :)

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