Question

Assume the triangle has the given measurements. Solve for the remaining sides and angles

A=(π/6,a=17.4,b=19.6

Answer 1

I know that B=178.4, but I don't know how to find C and c

Answer 2

@mtbender74

Answer 3

Do you know the law of sines?

Answer 4

yeah. Also I calculated 178.4 and I believe it is right, but it could be wrong lol

Answer 5

so using the law of sines, you should be able to get each other piece...start by getting angle B which will then get you angle C.
Once you have angle C, you can find side c...

So my approach would be
\[\frac{ \sin A }{ a } = \frac{ \sin B}{b}\]
solve that for B

then \[C = 2\pi - A - B \]

then \[\frac{\sin A}{a} = \frac{\sin C}{c}\]
solve that for c.

Answer 6

i assume that your angles are intended to be radians...that's why i used 2pi

Answer 7

is B=178.4

Answer 8

haven't worked it out...lemme check

Answer 9

no...were you using degrees or radians for your sin calculations?

Answer 10

I got 178.4 degrees

Answer 11

however it is A=pi/6 so it should be radians I think

Answer 12

3.11 radians

Answer 13

exactly...

lemme set it up for you.

\[\frac{\sin A}{a} = \frac{\sin B}{b}\]
\[\frac{\sin{\frac{\pi}{6}}}{17.4} = \frac{\sin B}{19.6}\]
\[\frac{.5}{17.4} = \frac{\sin B}{19.6}\]

make sure your calculator is in radians mode and find B...

Answer 14

oh...not exactly on 3.11 radian...

Answer 15

3.11366739

Answer 16

hmmm...i'm getting .6

Answer 17

pi/6 is not exactly .5 though I would rather use .52

Answer 18

sin pi/6 = .5

Answer 19

ah ok so .6 seems correct for B

Answer 20

so now, you can find C = 2pi - A - B

Answer 21

what is .6 is radians or do I just leave the answer as 0.6?

Answer 22

it is 0.6 radians...

Answer 23

1 radian is about 60 degrees

Answer 24

does B=0.6 or sinB=0.6 because sinpi/6 is different than pi/6

Answer 25

B = 0.6 radians...

Answer 26

Ok got it. so C=5.16

Answer 27

that's what i got too...

so now you have
\[\frac{\sin A}{a} = \frac{\sin C}{c}\]
\[\frac{\sin \frac{\pi}{6}}{17.4}=\frac{\sin 5.16}{c}\]

solve for c...

Answer 28

c=19.8? @mtbender74

Answer 29

actually...our C is wrong...it should be pi - A - B...my mistake...

Answer 30

sorry...

Answer 31

2.02 = C? are you sure?

Answer 32

yeah..was trying to figure out why it wasn't working

Answer 33

and that makes more sense with the answer i just got...

sin 2.02 = .9

Answer 34

so what is c?

Answer 35

\[\frac{\sin(pi/6)}{17.4}=\frac{\sin 2.02}{c}\]
\[\frac{.5}{17.4}=\frac{.9}{c}\]

solve for c

Answer 36

c=31.32. Ok, so overall the answers are B=0.6, C=2.02, and c=31.32. Correct?

Answer 37

@mtbender74

Answer 38

matches close enough to what i got...and the numbers make sense...

Answer 39

lol so it is right? what did you get that was different

Answer 40

c = 31.35...but i used the value from the calculator before rounding...

Answer 41

would my answer be graded wrong lol

Answer 42

as long as you show that you used .9 in the calculation *i* wouldn't if i were your teacher...and I was a teacher once upon a time... :)

Answer 43

got it, thanks. maybe you can help sometime later!

Answer 44

if i'm around...