Studying up for the FS and came across two separate double proportioning questions. The second question (#75) uses the cardinal equivalents along true bearings to proportion. The first question (#69) doesn’t. Can someone shed some light on this? I’m probably missing something very basic but can’t wrap my head around when to use trig to get the 89 degree bearing like in question 75 and when not to.
First pic is of question 69, second pic is of the solution for 69, third pic is question for 75, fourth pic is of solution for 75.
Question 69 is a double proportion, (you will be proportioning in two directions, the north-south line, and the east-west line, separately so to speak). You can use the cardinal offset which is the same as proportioning the east-west line and using that calculated easting, and then proportion the north-south line and use that calculated northing.
Question 79 is a single proportion, (the missing point is on-line and you are proportioning in one direction only), and as stated in the solution any excess or deficiency will be left to the unlabeled lot. Therefore Point ‘A’ is at 200 feet on-line from the northwest block corner to the northeast block corner.
Before someone else chimes in, Q79 is not really proportioning in this instance.
Hope this helps.
An abbreviation of the ‘solutions’:
Delta Lat = (distance) x (cosine of bearing)
Delta Dep = (distance) x (sine of bearing)
@cv thank you for the explanation. That all makes sense. And yes, after reading through your explanation for question 79 you are simply offsetting the point 200 ft from the northwest block on the same azimuth of the line.
From the OP question cardinal equivalents will be applied to question 69 after referencing the original plat.
Since the original plat isn't available and no basis of bearings are shown for the coordinates, the question is treated as a kinda real worldish question and hence the solution is B using simple check book math.
Here is a real world plat for the same township area from a township in eastern Wyoming:
As you can see the line between 5 and 6 has a 1d26' bearing and the line between 6 and 7 has a 89d18' bearing, the other bearings are north and west and no cardinal equivalents are needed to be calculated. To figure the cardinal equivalent for those dimensions apply sine and cosine to those bearings and you get 2639.17' between the SW corner of 5 and the 1/4 corner between 5 and 6, and the distance along the south line of 6 will become 5345.60' instead of 81 chs or 5346.00'. The cosine of 1d26' x 2640'=2639.17' and is the cardinal equivalent needed to do a double proportion for the SW of 5. If the example above had the same bearings given the answer would not be B, it would be slightly north and west of B.
Also, the basis of bearings for the coordinates need to be known and everything needs to be adjusted to "true north" for the proportion calculation.