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Q: 4 questions ( Answered 5 out of 5 stars,   3 Comments )
Subject: 4 questions
Category: Science > Math
Asked by: yalexa10-ga
List Price: $70.00
Posted: 11 Jun 2006 18:43 PDT
Expires: 11 Jul 2006 18:43 PDT
Question ID: 737328
4 trig questions

From the intersection of Simpson?s Road and Mulberry Lane proceed
"North 32 degrees West" for 320m along Simpson?s Road, then "Soutn 56
degrees West"  for 280m to the old oak tree, then "Soutn 22 degrees
East"  until Mulberry Lane is reached, and finally "Nortn 68 degrees
East"  along Mulberry Lane back to the starting point.

1.	Select an appropriate scale for the measurements (examples:
1/4=10cm  or 1cm=20m ) and draw a sketch of the property on one sheet
of regular size notebook paper. Label all the parts.

2.	Calculate the length of all sides of the property to the nearest
hundredth of a meter and the measures of all vertex angles to the
nearest tenth of a degree.  (Show work).  Incorporate these
measurements into your drawing.

3.	  Calculate the area of the property to the nearest square meter.  (Show work). 

4.	If the property tax rate in this county is $500 plus $175 for each
quarter hectare or portion thereof, calculate the property tax bill
for this property. (Show work)

Request for Question Clarification by redhoss-ga on 12 Jun 2006 05:49 PDT
Right after I commented last night I noticed that the question was
locked. I assumed that some ambitious person had answered. However, I
see that your question remains unanswered. I am too lazy to solve the
problem by hand, but as I said in the comment, I can give you all of
the lengths, angles, and the answer to part 4. Are you interested.

Clarification of Question by yalexa10-ga on 12 Jun 2006 11:56 PDT
Could you please give me the information that you have redhoss? I am
still interested. Thanks!
Subject: Re: 4 questions
Answered By: tox-ga on 14 Jun 2006 18:39 PDT
Rated:5 out of 5 stars

The answer to your 4 questions can be found in:


yalexa10-ga rated this answer:5 out of 5 stars

Subject: Re: 4 questions
From: redhoss-ga on 11 Jun 2006 19:44 PDT
I did a CAD layout of what I understand your problem to be. The area
appears to be 87,094.22 sq. meters. You could get all the angles and
lengths off the layout.
Subject: Re: 4 questions
From: activealexaoki-ga on 12 Jun 2006 10:37 PDT
Okay, I worked it out. Although the calculations were tedious, it
works and you will be able to obtain value for all the question.
(Assuming that the "all sides of property" means the distances
travelled for each direction. In this case they ask for only the
direction he travelled after the old oak tree because others are
already given?) My method is tedious because I focused on solving
rather than convenience. So I will write the method and will let you
calculate because I prefer not to work with a calculator.

1 : I believe you could have at least drawn a diagram.
2 : (Angles) From the starting point: 80 (56+32) (180-22-56) and
(22+68). The hint is to utilize the parallel lines (which in this case
is used to refer the angle of direction headed by the person) The
angle of 32 degrees, of 22 degrees, and of 56 degrees are able to
equate with other (respective) angles.
i. Drawing additional lines and EXTRA LABELS:
For this question the graph is cruicial but I assume you have that.
Suppose: from the starting point, label (a), (b) - first turn, (c) -
the old oak tree, (d) - reaching Mulberry Lane again. First draw
vertical line down from (b) and horizontal line to the right of (c)
until crossing the path (a)(b) - let the the distance until reaching
the path (a)(b) be called G and the intersection be called (e). and
the intersection of the vertical and horizontal be called (f). You
will then see smaller triangle (b)(f)(e). Let the hypothenus be now
called H, then the rest of length is 320-H. Next I want to connect (a)
and (c), and let the distance be called K. Lastly, label the angle
between G and K be "thetha".

ii. Finding K:
First, find the length of D. According to the pythagorean theorem (for
general triangle, not restricting to the right triangle) G can be
defined as:
G^2 = 280^2 + H^2 - 2(280)(H)cos(56+32)
therefore K can be expressed with G and 320-H by, again, the general
pythagorean theorem
K^2 = G^2 + (320-H)^2 -2(G)(320-H)cos(180-(90-32))
The angle for above equation can be simply found by using the smaller
triangle I earlier formed. The form is simple but contains two
variables. So you will need at least one more equation to express K
but in a different shape. Observer that you see another triangle
(a)(b)(c) K is the opposite of the nagle (56+32) Thus the K is written
K^2 = 280^2 + 320^2 - 2(280)(320)cos(56+32)
By solving the system of equations, you should be able to obtain both K and H.
Now, to get to the two sides you need (I assume) to find out, "theta"
because I will be using trig functions. Once again using the
pythagorean theorem, "theta" is easily defined:
(320-H)^2 = G^2 + K^2 - 2(G)(K)cos("theta")
320-H is known because H is known by previous system, G is known
because H is known by the first equation of G, K is known because the
system of equations allowed numerical value. Therefore there is really
only one variable, you can find it because there is exactly one
equation. After finding "theta", you will see the angle (d)(c)(a) is
102-(90-56)-"theta" and let it call T. Then two unknown sides are
(c)(d) = K*cos(T)
(d)(a) = K*sin(T) - forgive me if I confused sine and cosine
By the way, if you misunderstood, I mean product when I put integers
in parentheses. I usually don't write Asterisk for product, so
(320)cos(56+32) means 320 TIMES cosine of 88.
3. For the area of property, I suggest you use sine's - (area) =
(1/2)(adjacent side 1)(adjacent side 2)sin(Angle). You could possibly
use subtraction of triangles from rectangle, but you should decide. I
re-constructed three individual triangles, so you should be able to
calculate area of each triangle to find the total area of property.
4. Tax depends on the answer you give in 3.

Good luck
Subject: Re: 4 questions
From: redhoss-ga on 14 Jun 2006 18:56 PDT
Proper job tox-ga.

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