Question

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.

Answer 1

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

Answer 2

how do i do that

Answer 3

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

Answer 4

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

Answer 5

that is a link to 43 pages.

Answer 6

you have to scroll all the way down to the bottom

Answer 7

which page?

Answer 8

the very last one

Answer 9

43

Answer 10

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

Answer 11

yeah i think so but im not sure how

Answer 12

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.

Answer 13

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

Answer 14

yes, and we are looking for c

Answer 15

4^2+3^2=c^2

Answer 16

which equals 25

Answer 17

c^2 = 25
c = sqr(25)

Answer 18

5

Answer 19

yes, so label side AC with length 5

Answer 20

ok got it

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

ok

Answer 25

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 ?

Answer 26

we use law of cosine?

Answer 27

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 ?

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

and i got 25.1 but i have to square root it

Answer 32

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

Answer 33

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

Answer 34

i got 25 still

Answer 35

so what is side AD ?

Answer 36

well when i square root 25 i got 5

Answer 37

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.

Answer 38

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

Answer 39

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

Answer 40

yes

Answer 41

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?

Answer 42

no i dont know anything about the middle angle

Answer 43

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

Answer 44

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 ?

Answer 45

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

Answer 46

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

Answer 47

so then sin=a/sinA=b/sinB

Answer 48

yes. can you find angle ADE ?

Answer 49

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

Answer 50

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
\[ \frac{\sin A}{a} = \frac{\sin B}{b}\]

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

oh ok and then sin(38.845 is equal to 0.62 so you have \[\frac{ 7.8102 }{ ?sinA}=\frac{ 5 }{ 0.62 }\]

Answer 55

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)

Answer 56

0.6277524996

Answer 57

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

Answer 58

i put that in and it says error

Answer 59

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

Answer 60

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