Given A 80 degrees Side b 16 Side c 12 FInd the remaining

Given A = 80 degrees, Side b = 16, Side c = 12. FInd the remaining angles and side of the triangle.

Solution

Given that A = 80^o , b = 16 , c = 12

Using cosine rule

a² = b² + c² - 2bc cos(A)

==> a² = 16² + 12² - 2(16)(12) cos(80^o)

==> a² = 333.3191

==> a = (333.3191) = 18.257

==> a = 18.26

using sine rule

a / sinA = b/sinB = c/sinC

==> a / sinA = 18.26 / sin(80^o)

==> a / sinA = 18.54

==> b/sinB = 18.54

==> sinB = b/18.54

==> B = sin^-1(b/18.54)

==> B = sin^-1(16/18.54)

==> B = 59.66^o

sum of angles in a triangle = 180^o

==> C = 180 - (A + B)

==> C = 180 - (80 + 59.66)

==> C = 40.34^o