Question

Could someone please check this for me?!

I'll attach a picture of the triangle below, i just need to make sure i get this right!

A= pi/6, b=32.6, and c=41.4 are the given answers, in the end I came up with these:

A= pi/6, a=77.6, B=12.49 , b= 32.6, C=166.99, c=41.4

Answer 1

the question needs the law of cosine to find the value of a.

that seems to be the only unknown you need to find....

so

\[a^2 = 32.6^2 + 41.4^2 - 2 \times 41.4 \times 32.6 \times \cos(\frac{\pi}{6})\]

Answer 2

but you need to find a, before you can find any angles.... which would nee the law of sines...to find 1 angle, then angle sum of a triangle to find the other.

Answer 3

when i calculated that for a i got 77.6, would that be correct? @campbell_st

Answer 4

well I didn't get that.

Answer 5

I think you need to look at my calculation

Answer 6

how about 8.81? @campbell_st

Answer 7

well you're getting closer...

go back to my solution and type it into a calculator then way its written...

an each option might be to use pi/6 = 30 degrees

Answer 8

okay this time i did it and got 20.95 originally and then took the square root of that to get 4.58? @campbell_st

Answer 9

20.95 is the correct answer...

if you do the calculation you get

a^2 = 439.075

so

a = 20.9541

Answer 10

thank you! and from there could you maybe tell me how we'd find the angle measurement for B and C, unless by chance I got it right before! @campbell_st

Answer 11

ok to find the angle measures for C, use the law of sines

\[\frac{\sin(C)}{41.4} =\frac{ \sin(\frac{\pi}{6})}{20.05}\]

solve for C


when you get C you can find B by just using angle sum of a triangle.

Answer 12

when i do that, i get .0189, do i need to convert that to something else or am i just completely off track again? sorry for all the questions! @campbell_st

Answer 13

there is a typo in the calculation it should be

\[\frac{\sin(C)}{41.4} = \frac{\sin(\frac{\pi}{6})}{20.95}\]

then

\[C = \sin ^{-1}(0.253019)\]