Intersection.... how would u do this?
the following clock wise angles were observed:
at A from B to P the angle is 64d 42m 42s
at B from A to P the angle is 296d 15m 31s
the co-ordinates of A are 500E 500N
the co-ordinates of B are 703.501E 240.809N
Find the co-ordinates of P
I have added two points:
C is due north of point P &
C is due west of point A
D is due east of A
Points D, A, & C all have north coordinate of 500.000
The difference of the Northing coordinates from A to B:
( 240.809N - 500.000N ) = -259.191
The difference of the Easting coordinates from A to B:
( 703.501E - 500.000E ) = +203.501
The distance AB can be computed:
At this moment you should calculate the angle DAB
since it will be needed later:
[NOTE: We know that DAB is a negative angle, but that attribute will be ignored]
Angle CAP = 180d - ( 51d 51m 47s ) - ( 64d 42m 42s) = 63d 25m 31s <- NEED THIS!
Angle APC = 90d - ( 63d 25m 31s ) = 26d 34m 29s <-- do not need this but there it is.
You are given the interior angle BAP = 64d 42m 42s
The interior angle at B is 360d - (296d 15m 31s) = 63d 44m 29m
The third angle at P is: 180deg minus angles A & B
180d - (64d 42m 42s) - (63d 44m 29m) = 51d 32m 49s
Using the Rule of Sines (or The Law of Sines, or Sine Law)
which leads to
We do not require the distance BP.
The northing coordinates of P:
North coord of A MINUS distance AP x sin(angle CAP)
The easting coordinates of P:
East coords of A MINUS distance AP x cos(angle CAP)
Run this and determine the values.
I will do the math parts later as a check.
From the image it is clear that Point P is SOUTH & WEST of Point A.
If you do not have the visual aid, it is imperative to be cognizant of the signs of the computed values.