Question

@satellite73 Please help me with this one too! =)

Given triangle ABC with a = 7, C = 37°, and B = 18°, find c. Round the answer to two decimal places.
a. 13.63
b. 5.14
c. 18.56
d. 3.59

Given triangle ABC with b = 2, c = 4, and measure of angle A= 118 degrees, find a. Round the answer to two decimal places.
a. 4.87
b. 3.53
c. 3.26
d. 5.25

Answer 1

let me get to a real computer

Answer 2

Okay! Thanks!

Answer 3

law of sines for the first one
lets draw a reasonable triangle

Answer 4

Okay!

Answer 5

what is angle A?

Answer 6

I think Angle A= 125 degrees.

Answer 7

yeah \(180-37-18=125\) good
now use the law of sines to find c
\[\frac{c}{\sin(37)}=\frac{7}{\sin(125)}\iff c=\frac{7\sin(37)}{\sin(125)}\] and a calculator

Answer 8

Alright! =)

Answer 9

let me know what you get

Answer 10

Okay! I'll start solving it!

Answer 11

Alright! I got 5.14.

Answer 12

Thank you for your help!

Answer 13

Could I get help with the second problem? I'm really bad at this stuff!

Answer 14

yeah but i have to draw a picture first

Answer 15

you should too

Answer 16

Okay I will

Answer 17

i will wait for yours and then show you my picture

Answer 18

Okay, it's posted now.

Answer 19

ok now i get to be a bit critical, so don't take it the wrong way
look at your angle 118
does it look like at 118 degree angle?

Answer 20

i said that to one person one time and he got angry, but i don't mean it that way
it is good to be able to draw a somewhat accurate picture
it doesn't have to be exact, but it should be reasonable

Answer 21

Okay I'm sorry.

Answer 22

no no don't be sorry
i just mean it will be easier if you draw a picture that represents the triangle
one thing for sure, the 118 degree angle has to be larger than a 90 degree angle

Answer 23

Alright, I'll draw another one.

Answer 24

ok then i will show you the one i drew if i can still find it

Answer 25

nicer

Answer 26

but we still have a problem
the triangle is drawn correctly but the sides are not labelled correctly
the side opposite angle A is a
the side opposite angle B is b
the side opposite angle C is c

Answer 27

Oh oops! Should I draw another?

Answer 28

you have c opposite angle A

Answer 29

lets try to modify the one you have

Answer 30

no that wont work
let me draw one and explain

Answer 31

now like your second one, 118 looks reasonable
but here the sides are labelled opposite the corresponding angles
also notice that the side of length 4 is approximately twice the side of length 2
that is why your second picture cannot work as well

Answer 32

if it is ok with you, i am going to delete your third picture, because although it is labelled correctly, the lengths of the sides are not right

Answer 33

That's fine go head!

Answer 34

ok take a look at the picture i drew and notice that 2 is in fact shorter than 4, which is a good thing right?

Answer 35

i mean it probably should be even shorter, but at least it is not the same size or larger
this tells us that angle B will be the smallest angle, because it is opposite the smaller side

now i forgot what side we were looking for, although we can get all angles and all sides

Answer 36

We're looking for side a.

Answer 37

ok fine
first notice that if we were lucky we could use the law of sines, but we cannot in this case
is it clear why?

Answer 38

Yes it is.

Answer 39

if we try it, we would say
\[\frac{a}{\sin(118)}=\frac{2}{\sin(B)}\] but we need 3 of the 4 numbers to solve and we only have two of the four
so we need law of cosines

Answer 40

in this case use
\[a^2=b^2+c^2-2bc\cos(A)\] which in this specific example is
\[a^2=2^2+4^2-2\times 4\times \cos(118)\]

Answer 41

i get \(a^2=23.76\) rounded, making \(a=\sqrt{23.76}=4.87\) again rounded

Answer 42

i hope that is one of your choices
also i hope that it is clearer how to do these

Answer 43

Okay, thank you for your help.

Answer 44

yw

Answer 45

I now understand how to find the answer.

Answer 46

kk good luck