Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13 Trigonometric Ratios and Functions - Chapter Review - Page 900: 19

Answer

See below

Work Step by Step

We are given: $B,b,c$ Use law of sines to find, $\frac{\sin C}{c}=\frac{\sin B}{b}\\\sin C=\frac{\sin B}{b}\times c\\C=\arcsin(\frac{\sin B}{b}\times c)\\C\approx44.32^\circ $ Since the sum of the angles of a triangle is 180 degrees: $$A+B+C=190^\circ\\C=180-A-B\\=180-104-44.32=31.68^\circ$$ Find a: $\frac{a}{\sin A}=\frac{c}{\sin C}\\a=\frac{c}{\sin C}\times \sin A\\A=(\frac{18}{\sin 44.32 ^\circ}\times \sin 31.68^\circ)\\a\approx 13.53^\circ$
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