Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 1 - Review Exercises - Page 43: 16

Answer

$\theta=\beta-\alpha$

Work Step by Step

As we know that the angles $\gamma$ and $\beta$ are supplementary angles therefore $\gamma+\beta=180^{\circ}$ $\implies \gamma=180^{\circ}-\beta$.......eq(1) Similarly, we also know that the sum of all three angles of a triangle is $180^{\circ}$ that is $\alpha+\gamma+\theta=180^{\circ}$ Putting value of $\gamma$ from eq(1) in above equation, we obtain: $\alpha+180^{\circ}-\beta+\theta=180^{\circ}$ This can be rearranged as $\theta=180^{\circ}-\alpha-180^{\circ}+\beta$ This simplifies to: $\theta=\beta-\alpha$
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