I currently have a lot of things going on for college, so i cant get my brain settled into figuring this out. (I stay up until 4am almost every morning studying). My question is interesting but not so hard to achieve.
Im attaching the diagram here:
Task 1:
A farmer has a field as shown in the diagram, where AB,BC,CD and AD are all boundary fences. There are two straight line pathways in the field which run from A to C and B to D. There is also a quad bike track which is in the shape of an arc, also from B to D.
Your task is to identify all the missing key features (and their dimensions) of the field.
Task 2:
The farmer intends to build a new fence line across the field (labelled ABCD), to subdivide it to better manage the livestock and pasture ,which will start at point B and connect with the existing fence line AD. This new fence will then divide the field into a triangular section, towards the North, and a quadrilateral section, towards the South, of the original field.
The farmer would like the area of the triangular section to be between a half and a third of the area of the whole field.
Your task is to recommend to the farmer where the new fence should be built. Identify how far along the boundary fence AD that the new fence should be connected. The farmer would like to give you the reasons for your recommendation(s)
Formulas:
$\frac{a}{\sin a} = \frac{b}{\sin b} = \frac{c}{\sin c}$
$a^2 = b^2 + c^2 - 2bc \cos a$
$\cos A = \frac{b^2+c^2-a^2}{2bc}$
$\text{Area of triangle} = \frac{1}{2} bc \sin A$
$\text{Arc Length} = (\theta/360) \times 2\pi r$
$\text{Area of length} = (\theta /360) \times 2\pi r^2$
Thanks guys!