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: 23

Answer

$a=39.1$ in $c=134$ in $A=17.0^{\circ}$

Work Step by Step

Step 1: To find $a$, we use the formula $\tan\theta=\frac{b}{a}$. Step 2: $\tan73.0^{\circ}=\frac{128}{a}$ Step 3: $a=\frac{128}{\tan73.0^{\circ}}$ Step 4: Using a calculator, $a\approx39.13$ Step 5: Rounding the answer to three significant degrees, $a\approx39.1$ in. Step 6: To find $c$, we use the formula $\sin\theta=\frac{b}{c}$. Step 7: $\sin73.0^{\circ}=\frac{128}{c}$ Step 8: $c=\frac{128}{\sin73.0^{\circ}}$ Step 9: Using a calculator, $c\approx133.8$ Step 10: Rounding the answer to three significant degrees, $c\approx134$ in. Step 11: As $A+B=90^{\circ}$, $A=90^{\circ}-73.0^{\circ}$ Step 12: Solving, $A=17.0^{\circ}$.
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