Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 11 - Section 11.1 - The Sine Ratio and Applications - Exercises: 26


$\alpha\approx48^{\circ}$ $\beta\approx42^{\circ}$

Work Step by Step

$\sin\beta=\frac{2x}{3x}=\frac{2}{3}$ $\beta=\sin^{-1}\frac{2}{3}$ $\beta\approx42^{\circ}$ Sum of interior angles of a triangle $= 180^{\circ}$ $90^{\circ} + \alpha + \beta = 180^{\circ}$ $90^{\circ} + \alpha + 42^{\circ} \approx 180^{\circ}$ $\alpha\approx48^{\circ}$
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