SOLUTION: Stanbon, you are our hero!! We have an oblique triangle with angle B measuring 46.2 degrees. Side c measures 7.3, side b measures 10.3. The values given for sin(46.2) are 0.7218

Algebra ->  Trigonometry-basics -> SOLUTION: Stanbon, you are our hero!! We have an oblique triangle with angle B measuring 46.2 degrees. Side c measures 7.3, side b measures 10.3. The values given for sin(46.2) are 0.7218      Log On


   

Question 181607: Stanbon, you are our hero!! We have an oblique triangle with angle B measuring 46.2 degrees. Side c measures 7.3, side b measures 10.3. The values given for sin(46.2) are 0.7218, and for cos(46.2) is 0.6921. What is the value of sin C?
Found 2 solutions by Mathtut, Edwin McCravy:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
MATHTUT'S SOLUTION USING METHOD THAT LAW OF SINES WAS DERIVED FROM

ok!!!! we need to construct a line perpendicular to line BC coming from
vertex A .
:
we will call that distance h. This splits the triange into 2 right triangles.
:
sin 46.2=h/7.3
:
h=7.3(.7218)=5.27
:
sin C=5.27/10.3=highlight%28.5117%29

Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution using the law of sines:



Use the law of sines:

matrix%281%2C5%2Ca%2Fsin%28A%29%2C%22=%22%2Cb%2Fsin%28B%29%2C%22=%22%2Cc%2Fsin%28C%29%29

We are only dealing with the last two fractions:

matrix%281%2C3%2Cb%2Fsin%28B%29%2C%22=%22%2Cc%2Fsin%28C%29%29

Cross-multiply:

matrix%281%2C3%2Cb%2Asin%28C%29%2C%22=%22%2Cc%2Asin%28B%29%29

Divide both sides by b

matrix%281%2C3%2C%28b%2Asin%28C%29%29%2Fb%2C%22=%22%2C%28c%2Asin%28B%29%29%2Fb%29



matrix%281%2C3%2Csin%28C%29%2C%22=%22%2C%28c%2Asin%28B%29%29%2Fb%29

Substitute 7.3 for c, matrix%281%2C1%2C%2246.2%B0%22%29 for B,
and 10.3 for b and 

matrix%281%2C3%2Csin%28C%29%2C%22=%22%2C%287.3%2Asin%2846.2%29%29%2F10.3%29

Now get your calculator,

matrix%281%2C3%2Csin%28C%29%2C%22=%22%2C0.5115388024%29

Edwin