SOLUTION: ABC is a triangle in which SINA:SINB:SINC=7:8:10 and it's perimeter=75cm and m(B)=22 find it's area

Algebra ->  Triangles -> SOLUTION: ABC is a triangle in which SINA:SINB:SINC=7:8:10 and it's perimeter=75cm and m(B)=22 find it's area      Log On


   

Question 491873: ABC is a triangle in which SINA:SINB:SINC=7:8:10 and it's perimeter=75cm and m(B)=22 find it's area
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
The sides are going to be proportional to the opposite sine function. This is the law of sines.
a = 7/25 * 75 = 21 cm
b = 8/25 * 75 = 24 cm
c = 10/25 * 75 = 30 cm
21 cm + 24 cm + 30 cm = 75 cm.
This checks so we have the correct values for the sides.
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Now, we must use Herons formula to find our area.
Area == sqrt%28s%28s+-+a%29%28+s-b%29%28s-c%29%29
s = 21 + 24 + 30 / 2
s = 37.5
Area = sqrt%2837.5%2816.5%29%28+12.5%29%287.5%29%29
Area =sqrt%2858007.8%29
Area = 240.85 cm.
I am skeptical of the value you gave for the m(B) of 22. This value does not seem to fit with the rest of the data, I do not see where you can have a middle angle of 22 degrees with the sins in those proportions.
Cleomenius