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Don’t worry! Radians will be back before you know it! 11.2 The Law of Sines 763 B
h a c Q γ α α
A C b The remaining case is when ABC is a right triangle. In this case, the Law of Sines reduces to
the formulas given in Theorem 10.4 and is left to the reader. In order to use the Law of Sines to
solve a triangle, we need at least one angle-side opposite pair. The next example showcases some
of the power, and the pitfalls, of the Law of Sines.
Example 11.2.2. Solve the following triangles. Give exact answers and decimal approximations
(rounded to hundredths) and sketch the triangle.
1. α = 120◦ , a = 7 units, β = 45◦ 4. α = 30◦ , a = 2 units, c = 4 units 2. α = 85◦ , β = 30◦ , c = 5.25 units 5. α = 30◦ , a = 3 units, c = 4 units 3. α = 30◦ , a = 1 units, c = 4 units 6. α = 30◦ , a = 4 units, c = 4 units Solution.
1. Knowing an angle-side opposite pair, namely α and a, we may proceed in using the Law of
Sines. Since β = 45◦ , we get sin(45 ) = sin(120 ) or b = 7...
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