Question 1077706
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What is the length of angle <s>b</s> B and angle <s>a</s> A if given A = 150°, b = 4.8, a = 9.4?
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One of those is already GIVEN; so you need not to solve for the angle at point A.  



Draw your triangle and label all of the parts.  Understand, typically angle at point P will be opposite side p.  Do NOT confuse upper and lower case variable names!  You can expect angle at A is opposite side a.


Use Law of Sines to find angle measure at point B.
{{{sin(150)/9.4=sin(B)/4.8}}}


{{{4.8*sin(150)/9.4=sin(B)}}}


{{{sin(B)=(4.8/9.4)sin(150)}}}
Do you see that 150 degrees is {{{180-30}}} degrees and so the sine will be the same as for 30 degrees?


{{{sin(B)=(4.8/9.4)(0.5)}}}


{{{highlight_green(sin(B)=0.255191)}}}


Angle measure at point B,  {{{highlight(B=14.792*degrees)}}}


How to find angle measure at point C:
Sum of the interior angles must be 180 degrees.
{{{A+B+C=180}}}
{{{C=180-A-B}}}
{{{C=180-150-14.792}}}
{{{highlight(C=15.208)}}}


Already explained in a previous question posting, that you can use Law of Sines again to find length c.

{{{sin(C)/c=sin(A)/9.4}}}-----C and A are already known.


{{{sin(15.208)/c=(0.5)/9.4}}}
solve for c.