Question

What are the two cases in which the Laws of Sines can be applied to solve a non-right triangle?
Case I. You know the measures of two angles and any side of the triangle.
Case II. You know the measures of two sides and an angle opposite one of the two known sides.
Case III. You know the measures of two sides and the included angle.
Case IV. You know the measures of all three sides.
A. Case I and Case III
B. Case II and Case IV
C. Case III and Case IV
D. Case I and Case II

Answer 1

use a/sinA=b/sinB=c/sinC.....here a,b,c are sides and A,B,C are angles

Answer 2

i hate this question, it is a dumb thing to memorize. if you have a triangle and you want to solve it, the easiest way is to try and use the law of sines,
\[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\] but in order to do this you need two out of the three numbers
if you have them, you can do it, if you don't then you cannot

Answer 3

is it B

Answer 4

it is not B

Answer 5

or D

Answer 6

if you know only the three sides, then you do not know two out of the three numbers

Answer 7

its c

Answer 8

yes, it is D and you should draw a picture to see that if you are in case I then you know three out of the 4 numbers here, likewise for case II
\[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}\]

Answer 9

and the reason it is true for case I is that if you know two angles, you also know the third, since they have to add up to 180

Answer 10

I think its A...... For case || and |V we can't use law of sines........

Answer 11

im confused

Answer 12

yes you can. draw the picture and you will see it

Answer 13

okay let me think for a moment again.....

Answer 14

this is the law of sines
\[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}\]

Answer 15

in order for this to be of use, you have to know three out of the four numbers

Answer 16

Its not D I think so...... Because @satellite73 if we know two sides and the angle opposite to both the sides ....... Then we can't solve it..

Answer 17

if you know the angle opposite one of the sides, then if you call the side \(a\) and the angle opposite that side \(A\) then you know
\[\frac{\sin(A)}{a}\]

Answer 18

and if you know some other side, call it \(b\) then you know three out of the four numbers in \[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}\] so you can find the fourth

Answer 19

sorry messed it up a bit, yeah it's d

Answer 20

but as i said before, this is really a bad way to think about the law of sines. you should use it if you can, and you can tell easily if you can use it, by checking to see if you have three out of the four numbers

Answer 21

so what if i was law of cosine then it would be C

Answer 22

youhave six variables you know a,b,c i.e sides from case IV and two out of three angles A,B,C and then only one unknown angle remains which could be found by the sine law i had mentioned earlier.....hope it makes the picture clear

Answer 23

oh,okay..... I got it.thanks @satellite73 ..... :)

Answer 24

@akash809 if you know two out of three angles you would use the fact they add to 180

Answer 25

yeah noticed that there is no option of case I and Case IV and wouldn't make much sense too ,looks like i m not reading the options properly :)...time to sleep now