Trigonometry (11th Edition) Clone

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

Chapter 2 - Review Exercises - Page 95: 47

Answer

$a=32.38$ m $c=50.66$ m $B=50.28^{\circ}$

Work Step by Step

Step 1: To find $a$, we use the formula $\tan\theta=\frac{a}{b}$. Step 2: $\tan39.72^{\circ}=\frac{a}{38.97}$ Step 3: $a=38.97\times\tan39.72^{\circ}$ Step 4: Using a calculator, $a\approx32.376$ Step 5: Rounding the answer to four significant degrees, $a\approx32.38$ m. Step 6: To find $c$, we use the formula $\cos\theta=\frac{b}{c}$. Step 7: $\cos39.72^{\circ}=\frac{38.97}{c}$ Step 8: $c=\frac{38.97}{\cos39.72}$ Step 9: Using a calculator, $c\approx50.664$ Step 10: Rounding the answer to four significant degrees, $b\approx50.66$ m. Step 11: As $A+B=90^{\circ}$, $B=90^{\circ}-39.72^{\circ}$ Step 12: Solving, $B=50.28^{\circ}$.
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