Right on Tom!;-)
Now another.
The instrument station at point A is set up over the intersection of the centreline of the 30m wide road bearing 32°50'and the 20m wide road bearing 105°36'.
CB and BE are extensions of the road boundaries intersecting at B.
The centreline of the 20m road bearing 315° passes through point B.
Compute the bearing and distance of the setout lines from station A to corner points B, C, D and E.
It's actually a simple brg-brg intersect...
> disclaimer: In checking this I discovered a few centimeters of error. One or more of the angles has to bear some 'fluff'. The tank calcs 49.625 m at its closest proximity to the RW.
Sorry to be late to the party, but the above diagram shows the geometric construction. Based upon the information provided, the center of the tank is exactly at the intersection of the purple lines bisecting the angles indicated. Knowing the position of the center, the calculation of tank radius should be obvious and likewise the distance to the road line.
If worked correctly, the solution should be exact in that the radius of the tank will be the same, i.e. the distance from center to tangent will be the same, regardless of the choice of tangent to which the distance is computed.
Tom:
My reply was a bit quick.
The radius is 152.5
Area 784.3
Ok all you math whizzes...
Here's one for you:
Daddy owns 40 acres. He wants to keep the 10 acres with the house (as shown) and divide the remaining land equally among four children; with the stipulation that all four tracts be equal size and equal shape.
What are the dimensions of the 4 parcels to be given to the kids?
Ok all you math whizzes...
Ok all you math whizzes...
[sarcasm]You forgot the access easement for the one in the middle.[/sarcasm] 😀
> Tom:
> My reply was a bit quick.
> The radius is 152.5
> Area 784.3
You're correct. I think my radius distance was the same the first time, but I typed it wrong. The second time a calculated the area, I got 784.33. I think a few decimal square meters is rounding error and relatively immaterial.
I did it with a $3 calculator, and the answers I got were as follows:
Radius of the tank = 7.700m
Perpendicular offset from the tangency of the tank to the property line = 49.604m
I could only carry 5 decimal places with me with the calculator, so there could be some slight issues. However, AutoCad seems to agree with my $3 calculator to the thousandth of a meter so...... 🙂