In the triangle ABC

Question

AB=40cm AC=60cm cosB=-11/24

calculate the length of BC and the measure of angle A

 

Answer 1

draw the triangle. we can't use law of sines to find length BC directly. We can only find angle C. We're given cosB so from that we can find sinB using a calculator or a right triangle.

 

then sinB/60 = sinC/40

 

When we have angle C, we get angle A because the three angles add up to 180 degrees.

At this point we will have side-angle -side and can use the law of cosines to find side BC which is opposite angle A.

 

Hope that helps.

Answer 2

Cos(B)=-11/24

 

     B= 117.28

 

Using the formula

 

Sin (B)/b. =. Sin(C)/c

 

Sin(117.28)/60. = sin (C)/40

 

Sin (C)=(40/60)* sin(117.28)

           (2/3)*0.8887

           =0.5925

 

C= 36.33

 

A+B+C=180

 

So,

A = 26.39

 

Sin(A)/a= sin (C)/c

 

Sin(26.39)/a.  =sin (36.33)/40

 

a= 40 *Sin26.39 /Sin(36.33)

 

   =40*0.4445/0.5925

    = 30

 

So,

a=30

 

A=26.39 degrees

 

It is advisable that first you should draw the figure to better understand the problem.