SOLUTION: I need help understanding how to figure out a problem using the law of sines using only one angle measurement, 55, and two side measurements, 9 and 11.

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Question 133473This question is from textbook Geometry Applications and connections
: I need help understanding how to figure out a problem using the law of sines using only one angle measurement, 55, and two side measurements, 9 and 11.This question is from textbook Geometry Applications and connections

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
The law of sines only works for two sides and one angle if the angle is one of the non-enclosed angle. See diagram. If the 2 sides are a and b, and the angle is angle C, then the Law of Sines won't help you. But if you are given sides a and b and then either angle A or angle B, the Law of Sines works just fine.

drawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Atriangle%28-4%2C-2%2C-.5%2C3%2C3.5%2C-1%29%2C%0D%0Alocate%28-4.3%2C-2.3%2CA%29%2C%0D%0Alocate%28-.5%2C3.5%2CC%29%2C%0D%0Alocate%283.6%2C-1.1%2CB%29%2C%0D%0Alocate%28-2.8%2C1%2Cb%29%2C%0D%0Alocate%281.8%2C1.5%2Ca%29%2C%0D%0Alocate%28-.3%2C-1.9%2Cc%29%0D%0A%29
Let's say that the angle is angle A, side a is 9 and side b is 11.

The law of sines is:

a%2Fsin%28A%29=b%2Fsin%28B%29=c%2Fsin%28C%29


a%2Fsin%28A%29=b%2Fsin%28B%29
9%2Fsin%2855%29=11%2Fsin%28B%29

sin%28B%29=%2811%2Asin%2855%29%29%2F9

B=arcsin%28%2811%2Asin%2855%29%29%2F9%29


Then C=180-A-B, and you can calculate c by c=%28a%2Asin%28C%29%29%2Fsin%28A%29

I'll let you take care of the arithmetic.