How do you divide a 20 acre Parcel (in the shape of a triangle) into three equal parcels?

Question

This is a real life question. I own a twenty acre parcel. It was created by dividing a 40 acre parcel into two parcels by drawing a line from one corner of the one quarter mile by one quarter mile parcel (square) to another. Thus the twenty acre parcel is a triangle with a right angle and two equal sides each one quarter of a mile long. I need to divide it into three equal parts. I would like to divide it by drawing three lines from the right angled corner to intersect with the hypotenuse. The question is--at what angle/degree will each line be draw at to make three equal parts?

Answer 1

Divide the right angle into three equal parts, or three 30-degree angles.

Sounds like homework to me (which, hey, I'm cool with!), as if you owned this parcel this is NOT the way you'd want to divide it for real -- you wouldn't want three neighbors all bunched up like that at the confluence of the former right angle.

.

Answer 2

Well, the simple answer would be to trisect the hypotenuse. This is true because if you stand each triangle on the side that was the hypotenuse, each triangle would have the same base and the same height. By using the basic formula of ½ x base x height, and they would come out equal.

To determine the angles required, place your units along each side. The bottom is 440 feet long. the first trisected part of the hypotenuse is 440 * sqrt(2) / 3. This forms a smaller right angle with a 45° slope giving you the vertical line that meets this point. It is 440 / 3 feet tall. Now you have a right triangle with the angle that you want. It's "adjacent" side is 880/3, and it's opposite side is 440/3. Using the inverse tangent, you can find the angle, which is the inv tan(0.5) or approximately 26.565°. The lower and upper angles are equal, so the middle one is the result of subtracting twice this angle from 90, which is approximately 36.87°.

I hope this made sense...

Answer 3

Yes, a quarter-mile by quarter-mile lot makes 640/16=40 acres.
Now you have a triangular lot of 20 acres, made up of an isoceles right triangle of sides 440yds x 440 yds.

Your problem is easily solved if you stand the triangle on its hypotenuse, namely the height of the triangle equal to 440yds*sqrt(2)/2=approx. 311.127 yds.

You want to divide the lot equally into three parts by drawing TWO (not three) lines from the right angled corner to the hypotenuse.

By doing so, all three lots will have the height of h=311.127 yds, and so their bases should be equal!
You therefore draw lines from the right angled corner to the third points of the hypotenuse, namely 207.418 from each end of the hypotenuse.
As for the angle, it is not really important, as you can lay the points out using a tape (or chain), but I will provide it anyway.
Let a= the HALF angle, a, of the central lot
then tan(a)=207.418/2 /h=1/3
a=18.43494882 degrees, or
18 deg 26 min. 5.8 sec. (most theodolites are accurate to 3 seconds, so that should be accurate enough).
I will leave it to you to deduce the other angles.

Answer 4

i dont agree with the last two answers about dividing it into 3 equal angles because its a right triangle and thus the 2 ends will have more land

as u described with line coming to the hypotenus i got the center angle to be about 56 degrees while the side angles were like 62

Answer 5

one of two ways which will give you the same answer...
1) 90 degree right angle /3= 30degree angles
or
2)divide hypotenuse by 3 and connect the two points to the right angle

You would only need to draw 2 liines, not 3 to divide into 3 parts.

Answer 6

Simple. Divide the hypotenuse in to three equal parts, by marking two points on it. Then simply join the marked points to the right angled vertex, by drawing two st lines. You got your solution.

Answer 7

Since the two sides of the right triangle are equal, you can definitely trisect the right angle and it will divide your triangle into three equal-sized parcels.

•