• Step 3 Use the Law of Sines or the Law of Cosines to find m ∠ B . m angle b .

  sin B 6.2 ≈ sin 45 ° 5.56 Law of Sines sin B ≈ 6.2 sin 45 ° 5.56 Solve for sin B . m ∠ B ≈ sin − 1 ( 6.2 sin 45 ° 5.56 ) Solve for  m ∠ B . ( ∠ B  is not obtuse because  b < c . )   ≈ 52 ° Use a calculator . table with 4 rows and 3 columns , row1 column 1 , fraction sine b , over 6.2 end fraction , column 2 almost equal to . fraction sine , 45 degrees , over 5.56 end fraction , column 3 cap lawofcap sines , row2 column 1 , sine b , column 2 almost equal to . fraction 6.2 sine , 45 degrees , over 5.56 end fraction , column 3 cap solvefor sine b . , row3 column 1 , m angle b , column 2 almost equal to . sine super negative 1 end super . open . fraction 6.2 sine , 45 degrees , over 5.56 end fraction . close , column 3 cap solvefor . m angle b . . open . angle b . isnotobtusebecause . b less than c . . close , row4 column 1 , , column 2 almost equal to 52 degrees , column 3 cap useacalculator . . , end table

✓ Got It?

3. In Δ RST , s = 41 , t = 53 , cap delta and m ∠ R = 126 ° . m angle r equals , 126 degrees . What is m ∠ T m angle t ?

✓ Lesson Check

Do you know HOW?

1. In Δ ABC , m ∠ B = 26 ° , a = 20 cap delta in., and c = 10 c equals 10 in.

   Find b.

2. In Δ ABC , a = 8 m , b = 5 cap delta m, and c = 10 c equals 10 m.

   Find m ∠ A . m angle eh .

3. In Δ KNP , k = 21  cm  , n = 12 cap delta cm, and m ∠ P = 67 ° . m angle p equals , 67 degrees .

   Find m ∠ N . m angle n .

4. In Δ WXY , w = 7 . 7  ft  , x = 6.4 cap delta ft, and y = 8.5 y equals 8.5 ft.

   Find m ∠ W . m angle w .

Do you UNDERSTAND?

5. Writing Explain how you choose between the Law of Sines and the Law of Cosines when finding the measure of a missing angle or side.

6. Error Analysis A student solved for m ∠ C , m angle c comma for a = 11 eh equals 11 m, b = 17 b equals 17 m, and c = 15 c equals 15 m. What was the student's mistake?