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.

- anonymous

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- phi

we need more info. can you make a screen shot of the entire question?

- anonymous

how do i do that

- anonymous

https://www.georgiastandards.org/Georgia-Standards/Frameworks/Pre-Calculus-Unit-3.pdf

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## More answers

- 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

that is a link to 43 pages.

- anonymous

you have to scroll all the way down to the bottom

- phi

which page?

- anonymous

the very last one

- anonymous

43

- phi

ok. It sounds like they want all the angles and sides for each of the triangles

- anonymous

yeah i think so but im not sure how

- 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

so i would do a^2+b^2=c^2

- phi

yes, and we are looking for c

- anonymous

4^2+3^2=c^2

- anonymous

which equals 25

- phi

c^2 = 25
c = sqr(25)

- anonymous

5

- phi

yes, so label side AC with length 5

- anonymous

ok got it

- phi

the few pages in front of the last page seem to go through the solution

- anonymous

i saw that to but i dont really understand how they did that

- phi

Say the job is to find the sides of all 5 triangles.
so far you know the sides of triangle ABC

- anonymous

ok

- 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

we use law of cosine?

- 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

\[5^2+3.1623^2-2(5)(3.1623)\cos(71.5651\]

- phi

that is c^2
what do you get for c^2 and then c ?

- anonymous

dont you get 35.0-31.623*0.31 and then put that in the calculator?

- anonymous

and i got 25.1 but i have to square root it

- phi

I would use the calculator to do the whole computation
\[ 5^2+3.1623^2-2(5)(3.1623)\cos(71.565)\]

- phi

you don't want to round any numbers until the very end.

- anonymous

i got 25 still

- phi

so what is side AD ?

- anonymous

well when i square root 25 i got 5

- 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

so angle a is the same as angle c (71.5652)

- phi

If by angle a and angle c you mean < CDA and < ACD

- anonymous

yes

- 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

no i dont know anything about the middle angle

- 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

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

\[cosc=a^2+b^2-c^2/2ab\]

- 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

so then sin=a/sinA=b/sinB

- phi

yes. can you find angle ADE ?

- anonymous

remind me again is the a the side and the A is the degree right

- 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

ok \[\sin=\frac{ 7.8102 }{ sinA }=\frac{ 5 }{ \sin38.845 }\]

- phi

ok except I would not have that first sin = part
just
\[ \frac{ 7.8102 }{ \sin A }=\frac{ 5 }{ \sin38.845 }\]

- phi

typo:
\[ \frac{ 7.8102 }{ \sin A }=\frac{ 5 }{ \sin38.8845 }
\]

- 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

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

0.6277524996

- 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

i put that in and it says error

- phi

you can use google. type into the google search window
sin 38.8845 deg * 7.8102/5=

- anonymous

okay thank you for everything i got the rest your the best

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