Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.4 Solving Right Triangles - 2.4 Exercises: 24

Answer

$b=6.61$ m $c=14.3$ m $B=27.5^{\circ}$

Work Step by Step

Step 1: To find $b$, we use the formula $\tan\theta=\frac{a}{b}$. Step 2: $\tan62.5^{\circ}=\frac{12.7}{b}$ Step 3: $b=\frac{12.7}{\tan62.5^{\circ}}$ Step 4: Using a calculator, $b\approx6.611$ Step 5: Rounding the answer to three significant degrees, $b\approx6.61$ m. Step 6: To find $c$, we use the formula $\sin\theta=\frac{a}{c}$. Step 7: $\sin62.5^{\circ}=\frac{12.7}{c}$ Step 8: $c=\frac{12.7}{\sin62.5^{\circ}}$ Step 9: Using a calculator, $c\approx14.32$ Step 10: Rounding the answer to three significant degrees, $c\approx14.3$ m. Step 11: As $A+B=90^{\circ}$, $B=90^{\circ}-62.5^{\circ}$ Step 12: Solving, $B=27.5^{\circ}$.
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