Computing corner of a rounded plat map
March 8, 2024 5:48 PM   Subscribe

I have the map of a house lot that includes a curved corner. Based on the numbers & angles indicated on this excerpt of the plat map (linked here), how long are the orange lines in feet?

The plat map for a house lot has curved corners and weird angles. The long sides of the lot have a length indicated, but those distances in no way reach from the street in front to the back of the yard!

There must be some extra length implied by the curved corner....right? Assuming that, I need to figure out how long the oranges lines (which I added to the picture) are.

It looks to me like the letters say:
114.27' [this is the length of the front of the lot]
Δ = 93° - 37' - 00"
R = 15'
T = 15.98
L = 24.51'
Is R the radius of the corner? Are T and L the length of the orange lines?

(The neighbors told us that the builder who did this whole subdivision was sloppy with its paperwork, so I have a fear that I am about to wake a sleeping dragon.)
posted by wenestvedt to Home & Garden (6 answers total)
 
If that's a square, the orange lines are as long as the radius of the circle and therefore also 15'
posted by Vatnesine at 6:56 PM on March 8, 2024 [1 favorite]


Response by poster: That was my first instinct, but the angle is slightly acute.
posted by wenestvedt at 7:28 PM on March 8, 2024


Best answer: 15.98'
Horizontal Curve Equations
posted by Blue Genie at 7:38 PM on March 8, 2024 [2 favorites]


Best answer: L = 24.51' is the arc length of the curved arc. (To get this, convert the angle Delta to radians and then multiply by the radius R = 15'.)
posted by heatherlogan at 7:50 PM on March 8, 2024 [1 favorite]


(I should have previewed; Blue Genie has it, with a reference!)
posted by heatherlogan at 8:07 PM on March 8, 2024


The long term solution for this is to hire a professional surveyor to work backwards from established control points and definitively set the borders of your property
posted by rockindata at 10:52 AM on March 9, 2024 [1 favorite]


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