Question

Find all possible solutions for the triangle,
A=50º, a=15, b=12.

SOmeone please explain how to do this type of problem

Answer 1

law of sines yes? first step is to draw a reasonable triangle.

Answer 2

yes, ok done

Answer 3

you should have two triangles i think. do you?

Answer 4

why 2 triangles?

Answer 5

hold on one sec i will see if i can draw it for you somehow

Answer 6

http://upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Sine_Law_-_Ambiguous_Case.svg/400px-Sine_Law_-_Ambiguous_Case.svg.png

Answer 7

A = 50o
a = 12
b = 15
could look like this one exactly yes?

Answer 8

o, i just drew a simple triangle like this

Answer 9

yeah a little hard for me to see, but the image i sent you, that i just found by googling law of sines two triangles" looks pretty much exactly like what we are going to solve. so lets use that one

Answer 10

put
A = 50,
a = 12
b = 15

you can see that you can pivot the 12 side to make two triangles

Answer 11

first we solve for the big triangle like the one you drew.

Answer 12

law of sines gives
\[\frac{\sin(B)}{b}=\frac{\sin(A)}{a}\]
\[\sin(B)=\frac{b\sin(A)}{a}\]
\[\sin(B)=\frac{15\sin(50)}{12}\]

Answer 13

we want B not the sine of B so take the inverse sine of that mess
here i did it in one step
http://www.wolframalpha.com/input/?i=arcsine%2815+sin%2850+degrees%29%2F12%29

Answer 14

looks like B = 73.25

Answer 15

angle C is now easy since they have to add up to 180

Answer 16

180-50-75.25= 56.75

Answer 17

so we have
A= 50 a = 12
B = 73.25 b = 15
C = 56.75

Answer 18

and we can find c by using the law of sines again

Answer 19

and then you just do the law of cosine right?

Answer 20

oh no

Answer 21

law of cosines is a pain. only use it when you cannot use the law of sines

Answer 22

oo, ok

Answer 23

for c we just write
\[\frac{c}{\sin(C)}=\frac{a}{\sin(A)}\] and since we know 3 out of these 4 numbers we are good to go

Answer 24

\[c=\frac{12\sin(56.75)}{\sin(50)}\]

Answer 25

i get c = 13.1
http://www.wolframalpha.com/input/?i=12+sin%2856.75+degrees%29%2Fsin%2850+degrees%29

Answer 26

i think you used the length of b instead of a

Answer 27

really?

Answer 28

ya. a=15

Answer 29

damn damn damn

Answer 30

then first answer was wrong too!

Answer 31

i got c=16.38

Answer 32

o darn

Answer 33

ok we do it quickly now

Answer 34

i think i can figure out how to solve it now though. thank you!

Answer 35

\[\sin(B)=\frac{12\sin(50)}{15}\]
\[B=\sin^{-1}(\frac{12\sin(50)}{15})\]

Answer 36

http://www.wolframalpha.com/input/?i=arcsine%2812sin%2850+degrees%29%2F15%29
B=37.79

Answer 37

you good from here? this time there is only one triangle

Answer 38

yup, thanks!