SOLUTION: What is the length of angle b and angle a if given A = 150°, b = 4.8, a = 9.4? b = 14.794 * degrees C = 15.208 * degrees does b = 2,219°?

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Question 1077706: What is the length of angle b and angle a if given A = 150°, b = 4.8, a = 9.4?
b = 14.794 * degrees
C = 15.208 * degrees
does b = 2,219°?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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What is the length of angle b B and angle a 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%28150%29%2F9.4=sin%28B%29%2F4.8

4.8%2Asin%28150%29%2F9.4=sin%28B%29

sin%28B%29=%284.8%2F9.4%29sin%28150%29
Do you see that 150 degrees is 180-30 degrees and so the sine will be the same as for 30 degrees?

sin%28B%29=%284.8%2F9.4%29%280.5%29

highlight_green%28sin%28B%29=0.255191%29

Angle measure at point B, highlight%28B=14.792%2Adegrees%29

How to find angle measure at point C:
Sum of the interior angles must be 180 degrees.
A%2BB%2BC=180
C=180-A-B
C=180-150-14.792
highlight%28C=15.208%29

Already explained in a previous question posting, that you can use Law of Sines again to find length c.
sin%28C%29%2Fc=sin%28A%29%2F9.4-----C and A are already known.

sin%2815.208%29%2Fc=%280.5%29%2F9.4
solve for c.