Question

Help with law of sines

Answer 1

The information in the following problem allows you to construct 1 triangle. A = 30°, a = 1 m, b = 2 m

Answer 2

This is a true or false, but looking at it you should still be able to

Answer 3

you have all the points to get B

Answer 4

\[\frac{ 1 }{ \sin30 }=\frac{ 2 }{ sinB }\]

Answer 5

so find B using the law of sines...

find C using angle sum of a triangle...

see if they work...

smallest angle opposite shortest side etc

if that all works find c

Answer 6

\[B=\sin ^{-1}\frac{ 2\sin30 }{ 1}\]

Answer 7

B=30 degrees

Answer 8

180-30-30=120

Answer 9

C=120

Answer 10

\[\frac{ 1 }{ \sin30 }=\frac{ c }{ \sin120 }\]

Answer 11

so you have 2 angles of 30.. with sides of differing lengths... think about that

Answer 12

hmm Well that is 2 acute angles and one obtuse

Answer 13

ok... 2 equal angles... the sides opposite would need to be equal..?

check your calculations as I don't think B is 30

Answer 14

Sorry Back openstudy isnt loading

Answer 15

B=90?

Answer 16

I just realized since it was over 1 it is basically saying \[\sin ^{-1}(2\sin30)\]

Answer 17

C=60?

Answer 18

@campbell_st is 90 correctn?

Answer 19

90 is correct... so the triangle is right angled... the missing side can be found using pythagoras... and the missing angle using angle sum of a triangle

Answer 20

180-90-30=60 C=60

Answer 21

\[\frac{ 1 }{ \sin30 }=\frac{ c }{ \sin60 }\]

Answer 22

\[c=\frac{ \sin30 }{ \sin60 }\]

Answer 23

and use pythagoras 2^2 = 1^2 + c^2

Answer 24

so 4=1+c^2 c=sqrt3

Answer 25

So how could you see if you can only construct one or two triangles?

Answer 26

@freckles could you assist?

Answer 27

what was the first angle you solved for?

Answer 28

looks like it was angle B

Answer 29

I solved for angle B: which was 90

Answer 30

then got 60 for C

Answer 31

so you can see if there is a second traingle by doing \[B_2=180-B=180-90=90\]
But we see here we will have the same triangle if we check for the second triangle
so you have one triangle

Answer 32

So that means you cannot make another triangle since they have both the same angle?

Answer 33

when you double it?

Answer 34

if A and B were the same as before then C would have to be the same

Answer 35

this is the info given