Determine the area of the triangle The figure is not to scal

Determine the area of the triangle. The figure is not to scale. b=27 m, C=114 degrees, and B=34 degrees. What is the area of the triangle? (round to two decimal places)

Solution

B= 34 degree

C= 114 degree

b= 27 m

sum of all angles in a triangle = 180⁰

A+B+C = 180⁰

A = 180 - 34-114 = 32 degree

from Law of sine:

sin A/ a = sin B / b = sin C / c

take sin A/ a = sin B / b

sin 32⁰/ a = sin 34 / 27

after solving: a= 25.58 m

from sin B/ b = sin C / c

sin 34 / 27 = sin 114 / c

c = 44.10 m

from Hero\'s formula:

area = [ s( s-a) (s-b) (s-c)] ^1/2

s= a+b+c / 2

s= 25.58 + 27 + 44.10 / 2 = 48.34 m

area = [ 48.34 ( 48.34 - 25.58) ( 48.34 - 27) ( 48.34- 44.10) ]^1/2

= 315.51 m²