Exercises

Use the figure below for Exercises 1 and 2.

1. Below is the first step of a proof that sin A a = sin B b . fraction sine eh , over eh end fraction . equals . fraction sine b , over b end fraction . .

   1. h a b = h a b fraction h , over eh b end fraction , equals , fraction h , over eh b end fraction

      Complete the proof.

2. Below are the first three steps of a proof that a 2 = b 2 + c 2 − 2 b c cos A . eh squared , equals , b squared , plus , c squared , minus 2 b c cosine eh .

   1 ) b 2   = c 1 2 + h 2 2 ) c 2 = ( c 1 + c 2 ) 2 = c 1 2 + 2 c 1 c 2 + c 2 2 3 ) − 2 b c cos A = − 2 b ( c 1 + c 2 ) c 1 b = − 2 c 1 2 − 2 c 1 c 2 table with 3 rows and 4 columns , row1 column 1 , 1 close , column 2 b squared , column 3 , column 4 equals , c sub 1 and super 2 , plus , h squared , row2 column 1 , 2 close , column 2 c squared , column 3 equals . open . c sub 1 , plus , c sub 2 . close squared , column 4 equals , c sub 1 and super 2 , plus 2 , c sub 1 , c sub 2 , plus , c sub 2 and super 2 , row3 column 1 , 3 close , column 2 negative 2 b c cosine eh , column 3 equals negative 2 b . open . c sub 1 , plus , c sub 2 . close . fraction c sub 1 , over b end fraction , column 4 equals . negative 2 c sub 1 and super 2 . minus 2 , c sub 1 , c sub 2 , end table

   Complete the proof.

Use the Law of Sines to find the values of x and y. Round to the nearest tenth.

Use the Law of Cosines to find the values of x and y. Round to the nearest tenth.

Tell whether you would use the Law of Sines or the Law of Cosines to find the value of x. Then find the value of x. Round to the nearest tenth.

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