Question

please help

two boundary lines of a piece of property intersect at an angle 85 deg.. it is desired to cut off a triangular portion of the property which will be one acre (43560 sq. ft.) in area by means of a straight fence. If the fence begins at a point on one boundary 250 ft, from the corner of the property , and runs in a straight line to the other boundary , what does it make with the boundary lines and how long is it?

Answer 1

Draw a diagram. Let the 1-acre parcel be triangle ABC, with

B=85°
AB = 250
h is the altitude from AB to C
x is the length of side BC
y is side AC

250h = 43560
h = 174.24
h/x = sin85°
x = 174.91
y^2 = 250^2 + x^2 - 500x cos85°
y=292.36

x/sinθ = y/sin85°
sinθ = 174.91 sin85° / 292.36 = 0.60
θ = 36.6°

So, the fence is 292.36 ft long, making angles of 36.6° and 58.4° with the other sides.

Answer 2

rats - 1/2 * 250h = 43560
so, h=348.8

Adjust the other calculations accordingly. Good exercise for the student :-)