law of sines?

Question

Using the Law of Sines to solve the all possible triangles if

Angle A= 111
side a= 29
side b=11

Find the following:
Angle B=
Angle C=
side c=

Answer 1

a/sinA=b/sinB
sinb/11=sin111/29
angle b=20.7
angle c=180-111-20.7=48.3
c/sin48.3=29/sin111
side c=23.19

Answer 2

By the law of sines: (sinA)/ a = (sinB) / b = (sinC)/c.

so, sin 111 / 29 = (sinB) / 11 solve for sinB.
Angle B is arcsinB
Angle C is 180 - 111 - Angle B

and sin 111 / 29 = (sinC)/ side c.

That's the method, I'll leave the calculation as an exercise.

Answer 3

Sin 111/29 = Sin B/11 Note, sin 111=sin 69.
Once you have B, angle C= 180-(111+B). Then you can evalute c.

Answer 4

Hey there!

The Law of Sines can be found in this formula.

a/sin(A)=b/sin(B)=c/sin(C).

We know the following values.

a=29, b=11, A=111. Substitute these values into the formula, we get:

29/sin(111)=11/sin(B)=c/sin(C)

Let's solve for B.

29/sin(111)=11/sin(B) -->
11*sin(111)=29*sin(B) -->
10.27=29*sin(B) -->
sin(B)=10.27/29 -->
sin(B)=0.354 -->
B=arcsin(0.354) -->
B=20.73

Apply the Triangle Sum Property in order to find C.

A+B+C=180 -->
111+20.73+C=180 -->
131.73+C=180 -->
C=48.27

Apply the Law of Sines to find c.

29/sin(111)=c/sin(48.27) -->
(29/sin(111))*(sin(48.27))=c -->
c=23.2

So Angle B=20.73, Angle C=48.27, side c=23.2.

Hope it helps!

Answer 5

sin(angle B)/11 = sin(111)/29
sin(angle B) = 0.354116
angle B = 20.74 degrees

angle C = 180 - 111 - 20.74
angle C = 48.26 degrees

sin(48.26)/(side c) = sin(111)/29
sin(48.26)/(side c) = 0.354116
side c = sin(48.26)/0.03219
side c = 23.17