2— In reality, the polar visibility correction āyana-dṛkkarma; the adjustment for a planet's position relative to the celestial pole becomes precise through the planetary diurnal radius vimbīya-dyujyā; the radius of the circle representing the planet's daily path. It is as follows—

In the diagram provided below:—

In the planetary ecliptic-pole line kadamba-sūtra, Planet-Latitude = latitude śara = vertical leg koṭi.

In the planetary diurnal-pole line vimbīya-dhruvasūtra, Planet-Point A = hypotenuse karṇa.

In the ecliptic krāntimaṇḍala, Planet-Point A = base bhuja.

Thus, the arc Planet-A-Latitude forms a spherical right-angled triangle cāpa-jātya. Here, the mark 'A' The Sanskrit character 'अ' is used as a point marker in the diagram represents the planet as corrected for polar visibility.
Angle Planet-A-Latitude = 90°; Angle Point A-Planet-Latitude = arc of the polar planetary rod āyana-graha-yaṣṭi-cāpa.

Therefore:—

Radius trijyā : Rod yaṣṭi :: Sine of Hypotenuse : Sine of Latitude.

Planet-Y = Rod = vertical leg; K-Y = sine of polar deflection āyana-valanajyā = base.

Planet-K = Radius = hypotenuse.

Thus, Planet-Y-K is the first spherical right-angled triangle.

Diagram,

The diagram illustrates the celestial sphere with the ecliptic and the planet's path. It shows how the planet's latitude creates a small triangle against the coordinate grid of the sky, allowing astronomers to calculate exactly where the planet "appears" to be compared to its calculated position on the ecliptic.