Question

Given: 13 years ago

Answer 1

should we assume this is a traingle, and that you should employ the law of sines?

Answer 2

Isnt that a^2= b^2+c^c - 2ab( Cos A) Or something in that order.

Answer 3

thats the law of cosines :) that would be useful if the setup lends itself to it; but we may need the law of sines to begin with

Answer 4

sinA/a = sinB/b = sinC/c

Answer 5

Oh sorry.

Answer 6

if we used the law of cosines we would have 1 equation and 2 unknowns: c and C

Answer 7

so we cross multiply sinA , b and Sin B,a

Answer 8

\[a^2=b^2+c^2-2bc~cosA\]
\[a^2-b^2=c^2-2bc~cosA\]

c is stuck in a quadratic that may be difficult at the moment to unwrap.

yes, cross multiply to find B, then we know C = 180-(A+B)

and can find c

Answer 9

So \[\frac{ \sin(74) }{ 126}=\frac{ sinB }{ 84 }\]

Answer 10

sinB*126=80.7

Answer 11

\[c=\frac{2b~cosA\pm\sqrt{4b^2~cos^2A-4(b^2-a^2)}}{2}\]
\[c=\frac{2b~cosA\pm2b\sqrt{cos^2A+a^2}}{2}\]
\[c=b~cosA\pm b\sqrt{cos^2A+a^2}\]
\[c=b~(cosA\pm \sqrt{cos^2A+a^2})\]
:)

Answer 12

hmm, i almost did that ... but i factored out a b^2 from a^2; so it should prolly be\[c=b~(cosA\pm \sqrt{cos^2A+\frac{a^2}{b^2}})\]

Answer 13

lets do the sine laws, and see if we get about 156.65 :)

Answer 14

I get c = 158.3

Answer 15

\[sin^{-1}(\frac{ 84\sin(74) }{ 126})=B\]
\[180-(74+sin^{-1}(\frac{ 84\sin(74) }{ 126}))=105.304^o=C\]
\[c = \frac{a~sin(C)}{sin(A)}\]
\[c = \frac{126~sin(105.304)}{sin(74)}=126.43\]

Answer 16

is that what you have for c

Answer 17

i think so, let me try this simpler ....

B = arcsin(b sinA/a) = arcsin(84sin(74)/126) = 39.85 ....

C = 180 - 74 - 39.85 = 66.15

c = a sin(C)/sin(A) = 126 sin(66.15)/sin(74) = 119.885

Answer 18

sorry I lost connection, but ill check that one

Answer 19

119.885 is correct

Answer 20

But how do you know when to use the law sines or cosines

Answer 21

?

Answer 22

if i keep my number correct, the quadratic formula for law of cosines gives me 119.88 as well http://www.wolframalpha.com/input/?i=%28%282*84cos%2874%29%29%2Bsqrt%28%282*84cos%2874%29%29%5E2-4%2884%5E2-126%5E2%29%29%29%2F2

Answer 23

the law of sines is simpler, but can give a false reading in one particular setup

Answer 24

the law of cosine will always give you a correct answer

Answer 25

oh, so It really doesnt matter but its best to test both.

Answer 26

spose for the law of sines we only know A and c and a, we have 2 solutions for C and b

Answer 27

okay I think I see what your saying.

Answer 28

simplicity is best, but can lead to a false reading in a particular case.... so just be wary :)

Answer 29

okay Ill be sure to test my formulas! :)