Detemrine Lat Lon on ground from look down angle of aircraft

Hi.

I am trying to calculate the latitude and longitude of a point on the ground relative to an aircraft in flight based on the look down and side looking angles and range to the point on the ground.

I know the

latitude longitude of aircraft

side looking angle

elevation look down angle

slant range to particular point on the ground.

I suspect its all down to trigonometry but I don't really know where the start . Since my ranges can be quite large roughly 50km I suspect I will need to take the curvature of the earth into account in my calculations.

Any help much appreciated

Thanks