How Airborne Radar will know the angle of the Target Direction?

refer this http://faculty.nps.edu/jenn/Seminars/RadarFundamentals.pdf

The platform of the radar moves in direction of the x-axis. The radar “looks” with the looking angle θ (or so called off-nadir angle). The angle α between x-axis and the line of sight (LOS) is called cone angle, the angle φ between the x-axis and the projection of the line of sight to the (x; y)-plane is called azimuth angle. Cone- and azimuth angle are related by cosα = cosφ ∙ cosε. On the earth surface the wave comes in at the (nominal ellipsoidal) incident angle β with respect to the vertical axis at this point. (In some publications the incident angle is denominated to as θi.) The antenna illuminates an area, the so-called footprint. The direction of the incoming wave relative to the horizontal plane may be measured also. This angle γ = 90° − β is called grazing angle. The angle ϑ = ε + 90° is used for a mathematical description in a spherical coordinate system.

By using the Heading and Bearing and the Gps which located instead of it

The angular determination of the target is determined by the directivity of the antenna. Directivity, sometimes known as the directive gain, is the ability of the antenna to concentrate the transmitted energy in a particular direction. An antenna with high directivity is also called a directive antenna. By measuring the direction in which the antenna is pointing when the echo is received, both the azimuth and elevation angles from the radar to the object or target can be determined. The accuracy of angular measurement is determined by the directivity, which is a functionThe True Bearing (referenced to true north) of a radar target is the angle between true north and a line pointed directly at the target. This angle is measured in the horizontal plane and in a clockwise direction from true north. (The bearing angle to the radar target may also be measured in a clockwise direction from the centerline of your own ship or aircraft and is referred to as the relative bearing.)

The antennas of most radar systems are designed to radiate energy in a one-directional lobe or beam that can be moved in bearing simply by moving the antenna. As you can see in the Figure 2, the shape of the beam is such that the echo signal strength varies in amplitude as the antenna beam moves across the target. In actual practice, search radar antennas move continuously; the point of maximum echo, determined by the detection circuitry or visually by the operator, is when the beam points direct at the target. Weapons-control and guidance radar systems are positioned to the point of maximum signal return and maintained at that position either manually or by automatic tracking circuits.

In order to have an exact determination of the bearing angle, a survey of the north direction is necessary. Therefore, older radar sets must expensively be surveyed either with a compass or with help of known trigonometrically points. More modern radar sets take on this task and with help of the GPS satellites determine the northdirection independently. of the size of the antenna.

by calculating the difference of quadrant of transmitted and received energy 

Airborne Radar always update its position with a fixed point along its journey in order to place itself and targets accurately (to some extent), this is a simple interpretation but in reality the radars are supplied with electronic maps and live-on cameras by which they correlate with each other to position the target using a fixed point as I mentioned.