[DarkIxion]

A Gelert farmer owns a small farm just outside Meridell where he grows berries. His plot of land is a rather odd shape... it's in the shape of two overlapping squares, one at a 59-degree angle to the other. The larger of the two squares is 180 meters on a side, and the smaller of the two is 162 meters on a side. The corner point of the larger square is at the center point of the smaller square.

Since it's springtime, it's time for the farmer to start planting berries! So, in the area of his field that is only within the larger square, he's planting Jumbleberries, which take 3 minutes per square meter to plant. The area of the field that is only within the smaller square will be planted with Red Chiaberries, which take 4 minutes per square meter to plant. Finally, in the area where the two overlap, he's planting Voidberries, which take 5 minutes per square meter to plant.

The Gelert farmer wants to have his entire field planted in three days. Assuming each person can work up to 8 hours a day, how many people would be required to do so? Round up to the nearest whole number.




This has really got me stumped, I can't remember how to use the sine/cosine/tangent things either...

Can someone help? If I could see the working out of it too it may help me with my other questions...

[Dr_Calculus]

The key to this problem is finding the area of overlap. This can be done by connecting the two vertices that are right angles. This will create two triangles. If you can find the values for each angle, then you can probably use the law of sines or law of cosines to calculate the values of each side. Hope this helps.

[phr0ze]

I have drawn in two triangles. Solve these and the rest will fall in place. Hint after you know the two hypotnuses, go back to your original drawing, And connect the opposite corners than what were suggested by Dr. Calc. He may have a better solution in mind but for my diagram this is best.

[Dr_Calculus]

Good job phorze, I missed the fact that the corner was in the center. If you draw the diagonal of your 81ft square, then we will have the lengths of both the line connecting the two rt. Angles and the dotted line. Since we can easily find the angle measures, the problem is trivial using the laws of sine/cosine:

Law of sines: sinA/a=sinB/b=sinc/C

Law of Cosines: a^2=b^2+c^2-2bc(cosA)

where A is the angle opposite side a, B is the angle opposite side b, etc. I'll leave the calculating to you.

[Dr_Calculus]

Phorze, I didn't see something very significant before. Notice that the square has a rt. Triangle OUTSIDE the 81m square, and a rt. Triangle INSIDE the square. Upon closer inspection, I found the two to be CONGRUENT, which means the area of overlap IS 81^2. I cranked through the calculations (I found out how many minutes total it would have taken, divided by 60 to get to hours, divided by 8 to get to days, and divided by 3 to get how many people you would need.) I came up with 132. Anyone want to check me on that?