Question 1121144: City C has a bearing of N 32o E from city A, and a bearing of N 22o W from city B. City B is due east of city A, and is 24 miles from city C. Find the area of triangle ABC.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw this
ABC is the triangle. a is 24 b is 32 and angle A is 58, angle B 68, and angle C 54
From Law of Sines, 24/sin 58=b/sin 68=c/sin 54.
24/sin 58=28.30
b is 28.30 sin 68=26.24
c is 28.30 sin 54=22.90. c is the base
Can do the area from Hero's formula
S=(1/2)(A+B+C)=(1/2)(24+26.24+22.90)=36.57
S-A=12.57
S-B=10.33
S-C=13.67
A=sqrt (S*(S-A)(S-B)(S-C))=sqrt (36.57*12.57*10.33*13.67)=254.78 mi^2 ANSWER
Can check with side c=22.90, so altitude must be 509.56/22.90, or 22.25 mi
with one triangle, 26.24=alt/sin 58=22.25 mi
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