anonymous
  • anonymous
an antique map was found in the attic of a local courthouse. it shows some measurements from a local farm that was divided into 5 parts. some of the measurements have faded with age, so you must find the remaining measurements, as well as calculate the total area and perimeter of the outside property. all lengths are measured in miles.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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phi
  • phi
we need more info. can you make a screen shot of the entire question?
anonymous
  • anonymous
how do i do that
anonymous
  • anonymous
https://www.georgiastandards.org/Georgia-Standards/Frameworks/Pre-Calculus-Unit-3.pdf

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anonymous
  • anonymous
the question is on the link but its all the way at the bottom znd it has help on it but i dont understand it
phi
  • phi
that is a link to 43 pages.
anonymous
  • anonymous
you have to scroll all the way down to the bottom
phi
  • phi
which page?
anonymous
  • anonymous
the very last one
anonymous
  • anonymous
43
phi
  • phi
ok. It sounds like they want all the angles and sides for each of the triangles
anonymous
  • anonymous
yeah i think so but im not sure how
phi
  • phi
Mostly the Law of Cosines and Law of Sines Let's start in the lower right. that is a right triangle with sides 3 and 4 use pythagoras to find the hypotenuse.
anonymous
  • anonymous
so i would do a^2+b^2=c^2
phi
  • phi
yes, and we are looking for c
anonymous
  • anonymous
4^2+3^2=c^2
anonymous
  • anonymous
which equals 25
phi
  • phi
c^2 = 25 c = sqr(25)
anonymous
  • anonymous
5
phi
  • phi
yes, so label side AC with length 5
anonymous
  • anonymous
ok got it
phi
  • phi
the few pages in front of the last page seem to go through the solution
anonymous
  • anonymous
i saw that to but i dont really understand how they did that
phi
  • phi
Say the job is to find the sides of all 5 triangles. so far you know the sides of triangle ABC
anonymous
  • anonymous
ok
phi
  • phi
now look at triangle ACD. we have two sides and we need to find the 3rd side. Do we have enough info to do that ?
anonymous
  • anonymous
we use law of cosine?
phi
  • phi
yes. If we see side-angle-side with numbers, then we can use the Law of Cosines to find the unknown side. Do you know how to do that to find side AD ?
anonymous
  • anonymous
\[5^2+3.1623^2-2(5)(3.1623)\cos(71.5651\]
phi
  • phi
that is c^2 what do you get for c^2 and then c ?
anonymous
  • anonymous
dont you get 35.0-31.623*0.31 and then put that in the calculator?
anonymous
  • anonymous
and i got 25.1 but i have to square root it
phi
  • phi
I would use the calculator to do the whole computation \[ 5^2+3.1623^2-2(5)(3.1623)\cos(71.565)\]
phi
  • phi
you don't want to round any numbers until the very end.
anonymous
  • anonymous
i got 25 still
phi
  • phi
so what is side AD ?
anonymous
  • anonymous
well when i square root 25 i got 5
phi
  • phi
so label side AD 5 it looks like triangle ACD is isosceles (2 sides the same length) that means we know the base angles are both 71.5651 and the angle CAD is 180 - 2*71.5651 I am not sure we we to write that down, but we do know it.
anonymous
  • anonymous
so angle a is the same as angle c (71.5652)
phi
  • phi
If by angle a and angle c you mean < CDA and < ACD
anonymous
  • anonymous
yes
phi
  • phi
now triangle ADE we have 2 sides, and an angle, but it is the wrong angle. However, we can find the "middle angle". Any ideas how?
anonymous
  • anonymous
no i dont know anything about the middle angle
phi
  • phi
Do you see we want to find side DE ? to do that we can use side AE, angle DAE, side AD and the Law of Cosines but we need angle DAE
phi
  • phi
When I see we have sides and angles, and need an angle, I would try using the Law of Sines. What angle can we find if we use the Law of Sines ?
anonymous
  • anonymous
\[cosc=a^2+b^2-c^2/2ab\]
phi
  • phi
we can't use that because we don't know two things (angle C and side c) I would use the Law of Sines to find angle ADE
anonymous
  • anonymous
so then sin=a/sinA=b/sinB
phi
  • phi
yes. can you find angle ADE ?
anonymous
  • anonymous
remind me again is the a the side and the A is the degree right
phi
  • phi
yes, you can only take sines of angles. you can write the Law of Sines as \[ \frac{a}{\sin A} = \frac{b}{\sin B}\] or as \[ \frac{\sin A}{a} = \frac{\sin B}{b}\]
anonymous
  • anonymous
ok \[\sin=\frac{ 7.8102 }{ sinA }=\frac{ 5 }{ \sin38.845 }\]
phi
  • phi
ok except I would not have that first sin = part just \[ \frac{ 7.8102 }{ \sin A }=\frac{ 5 }{ \sin38.845 }\]
phi
  • phi
typo: \[ \frac{ 7.8102 }{ \sin A }=\frac{ 5 }{ \sin38.8845 } \]
anonymous
  • anonymous
oh ok and then sin(38.845 is equal to 0.62 so you have \[\frac{ 7.8102 }{ ?sinA}=\frac{ 5 }{ 0.62 }\]
phi
  • phi
it's sin 38.8845 (not 38.845) when you do the calculation you should keep at least 5 decimals (I would keep all that the calculator uses)
anonymous
  • anonymous
0.6277524996
phi
  • phi
The way I would do it is write it as \[ \frac{\sin A}{7.8102} = \frac{\sin 38.8845}{5} \] and then multiply both sides by 7.8102 to get \[ \sin A =\frac{\sin 38.8845}{5}\cdot 7.8102\] now use a calculator to find sin A
anonymous
  • anonymous
i put that in and it says error
phi
  • phi
you can use google. type into the google search window sin 38.8845 deg * 7.8102/5=
anonymous
  • anonymous
okay thank you for everything i got the rest your the best

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