trigonometry

Question

Determine the number of triangles that can be constructed with the given measures:

1) measure of angle A= 140 degrees, b=10, a=3

2) measure of angle A =118 degrees, b=11, a=17

3) measure of angle A = 30 degrees, a=13, b=16

Answer 1

1) A = 140    b = 10      a = 3

 

  a    = b    

SinA    SinB

 

  3   =  10   

0.64     SinB

 

 

B = Sin^-1( 6.4/3)  undefined , No triangle can be made with these data.

 

2) 17  = 11     

   0.88    Sin B

 

 B = Sin^-1 ( 11* 0.88 / 17) = 34. 7 °

 

C = 180 - ( 118 + 34.7) = 27.3°  Only one triangle

  

c = 11* 0.88/ Sin 27.3° = 21.10

 

3 )  13    = 16     

      1/2      Sin B

 

 B = 38°  or 142°

 

C = 180 -38-30 =112°    or 180 -142 - 30   = 8°

 

c = 8/ sin 8° = 57.48