Show the worlk to solve the oblique triangles where a11 b15

Show the worlk to solve the oblique triangle(s) where a=11, b=15, and c=21. Indicate the number of triangles. Round off all final answers to two decimal places. Put \"N/A\" on an answer line to indicate no answer. A1=, A2=, B1=, B2=, C1=, C2=. PLEASE answer all the above. Captial letters are the angle measures and lower case letters are the side lenghts of the triangle(s)

Solution

a=11, b=15, and c=21

Find first angle A :

Use cosine rule :

cosA = ( b^2 +c^2 - a^2)/2*b*c

= ( 15^2 +21^2 - 11^2)/(2*15*21)

=0.865

A = 30.10 deg

Use sine rule to find other angles:

a/sinA= b/sinB

sinB = b*sinA/a = 21*sin30.1/11 = 0.9657

B1 = 73.22 deg ; B2 = 180 - 73.22 = 106.77 deg

C1 = 180 -B1 -A = 76.68 deg ; C2 = 180 - B2 - A = 43.13 deg

Two traingles are possibel , one with AB1C1 and other with AB2C2