Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 893: 39

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Using Pythagorean theorem we find, $b=\sqrt a^2+c^2\\=\sqrt 15^2+6^2\\=\sqrt 261\\=3\sqrt 29$ Since $a=15, b=3\sqrt 29$, we obtain: $\sin A=\frac{15}{3\sqrt 29}\\A=\arcsin \frac{15}{3\sqrt 29}\approx68.2^\circ$ $\sin C=\frac{6}{3\sqrt 29}\\C=\arcsin \frac{6}{3\sqrt 29} \approx 21.8^\circ$