Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Review Exercises - Page 90: 49

Answer

$a=638$ $b=391$ $B=31^{\circ}30'$

Work Step by Step

Step 1: Converting the angle to decimal degrees; $58^{\circ}30'=58\frac{30}{60}^{\circ}=58.5^{\circ}$ Step 2: To find $a$, we use the formula $\sin\theta=\frac{a}{c}$. Step 3: $\sin58.5^{\circ}=\frac{a}{748}$ Step 4: $a=748\times\sin58.5^{\circ}$ Step 5: Using a calculator, $a\approx637.7$ Step 6: Rounding the answer to three significant degrees, $a\approx638$ Step 7: To find $b$, we use the formula $\cos\theta=\frac{b}{c}$. Step 8: $\cos58.5^{\circ}=\frac{b}{748}$ Step 9: $b=748\times\cos58.5^{\circ}$ Step 10: Using a calculator, $b\approx390.8$ Step 11: Rounding the answer to three significant degrees, $b\approx391$ Step 12: As $A+B=90^{\circ}$, $B=90^{\circ}-58^{\circ}30'$ Step 13: Solving, $B=31^{\circ}30'$
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