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: 25

Answer

$a=70.7$ cm $c=80.9$ cm $B=29.0^{\circ}$

Work Step by Step

Step 1: To find $a$, we use the formula $\tan\theta=\frac{a}{b}$. Step 2: $\tan61.0^{\circ}=\frac{a}{39.2}$ Step 3: $a=\tan61.0^{\circ}\times39.2$ Step 4: Using a calculator, $a\approx70.72$ Step 5: Rounding the answer to three significant degrees, $a\approx70.7$ cm. Step 6: To find $c$, we use the formula $\cos\theta=\frac{b}{c}$. Step 7: $\cos61.0^{\circ}=\frac{39.2}{c}$ Step 8: $c=\frac{39.2}{\cos61.0^{\circ}}$ Step 9: Using a calculator, $c\approx80.86$ Step 10: Rounding the answer to three significant degrees, $c\approx80.9$ cm. Step 11: As $A+B=90^{\circ}$, $B=90^{\circ}-61.0^{\circ}$ Step 12: Solving, $B=29.0^{\circ}$.
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