Finding all lengths

amathproblemthatneedsolve

amathproblemthatneedsolve

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May 12, 2019
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1. Find all the length of the below,

I found the length of the line AC=151.41, angle A in ACD was equal to 22.862 degrees

If I call the place where all the lines seem to intersect K than line DK is just the height from the base of triangle ACD and respectively for ABC so I found that with ACD height base being 56.4 I got line AK= 145. Using angle C in triangle ABC which is 20degrees I get line KB=61m

for the sector I did my angle of 100 degrees, the radius is 60m according to the graph, the diameter is 120m and arc length is 104.7198m. Note if it matters according to all my calculation the area is 3141.59m^2

Where I need help if the above is correct is with the second part,

they want to build a new fence across line ABCD. The fence will start at point B and connect with the existing line AD. The new fence will then divide the field into a triangular section, towards the north, and a quadrilateral section, towards the south. They want the area of the triangular section to be between a third and half of the area of the whole field .





Attachment-1.jpeg
 
lev888 said:
I don't know, I am asking why you concluded that DK is the height.
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I concluded that based on my statement...."DK is just the height from the base of triangle ACD" I should have included to the highest point in the triangle but that's self-explanatory if you look at the image. If the answer is wrong then I have made a mistake somewhere.
 
amathproblemthatneedsolve said:
I concluded that based on my statement...."DK is just the height from the base of triangle ACD" I should have included to the highest point in the triangle but that's self-explanatory if you look at the image. If the answer is wrong then I have made a mistake somewhere.
Click to expand...
Don't get it. What is you statement based on? You can't just say "this line is the height". Do you know what height is? Does DK qualify?
 
Ok, I'll explain it in a different way for you. Look at the triangle ACD, one side is 60m, one side is 120m and an angle is 110degrees and if you calculate that triangle Height, from base you get line DK or the height base of triangle ACD to be 56.4m.
 
Height is always measured perpendicular to the base. DK is not perpendicular to AC, so it is not the height of ACD. Lev888 is asking you to explain why you wrongly think it is, so we can help you abandon that wrong attempt, and find a correct way to solve the problem.
 
You don't know DK is perpendicular to AC. I get DK is 45.1 another way.
[Edit] Dr P apparently types faster than I do.
 
OH ok, I'm getting DK is 45m for some reason. I changed my approach I worked out the small triangle DBC and got angle D=40degrees (note line DB was 91.925) So using the angle 40-110=70degrees that's what I got for angle D on the other side knowing the side 120m and the angle A= 22degrees DK=45 . What am I doing wrong?
 
At the moment I'm just checking numbers against what I see on GeoGebra (rather than continue calculating everything); it looks like DK is a little less than 45 (44.7), and angle DAC is a little less than 22 degrees (21.86). And it happens that angle AKD is very close to 90 degrees (88.14). Are you reporting your numbers accurately?

It may help if you show your specific calculations.

Also, to check, you described K as "the place where all the lines seem to intersect". Of course, they do intersect! Are you, as I've assumed, referring to the intersection of lines AC and BD?
 
Firstly yes they are the same result I got I have just rounded them as I have been told too I should have stated that, sorry. Secondly yes I am referring to the intersection of lines AC and BD.
 
So I want to establish what current results for all the lengths are.

Line AC=151.41m, Line DK is 44.7m, Line DB is 91.925m meaning that KB is 47.225m, Line AK is 112.882, Line KC is 38.588, Line AB is 123.7, An length of the arc is 104.7.

Angles: Angle A is 21.86degrees, Angle K is 88.14degrees, Angle C is 48.14 degrees.

If this is all correct what do I do for the second part?
 
The second part, I believe, was

They want to build a new fence across line ABCD. The fence will start at point B and connect with the existing line AD. The new fence will then divide the field into a triangular section, towards the north, and a quadrilateral section, towards the south. They want the area of the triangular section to be between a third and half of the area of the whole field .​

Put a new point E on AD, at a point x units from A, and find the area of ABE. Determine what values of x will make this area 1/3 or 1/2 of the area of ABCD. It isn't clear exactly what is wanted, but anything between those two positions will accomplish the goal. There are several fairly easy ways you might do this; one is to find the area of triangle ABD, and think proportionally.
 
DBC Area = 1,772.65396

ABC Area = 5,181.43565

This means the area of the whole shape is 5,181.43565 + 1,772.65396= 6954.08961 1/2 of this is 3477.044805 or alternatively, 1/3 is 2318.02987.

So I could be wrong If I use the angle of A = approx 44degrees than line AE has to be 80.95m and line BA=86.304 and the area of ABE is 3477.986. this is a bit off so I think I might have done something wrong?
 
That sounds like the right values.

I'm not clear exactly how you did the calculation. The total area is not DBC + ABC, and I'm not sure how you are using the angle. But you probably did more or less correct work.
 
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