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: 21

Answer

$a= 8.17$ ft $b= 15.4$ ft $B=62.0^{\circ}$

Work Step by Step

Step 1: To find $a$, we use the formula $\sin\theta=\frac{a}{c}$. Step 2: $\sin28.0^{\circ}=\frac{a}{17.4}$ Step 3: $a=17.4\times\sin28.0^{\circ}$ Step 4: Using a calculator, $a\approx8.169$ Step 5: Rounding the answer to three significant degrees, $a\approx8.17$ ft. Step 6: To find $b$, we use the formula $\cos\theta=\frac{b}{c}$. Step 7: $\cos28.0^{\circ}=\frac{b}{17.4}$ Step 8: $b=17.4\times\cos28.0^{\circ}$ Step 9: Using a calculator, $b\approx15.36$ Step 10: Rounding the answer to three significant degrees, $b\approx15.4$ ft. Step 11: As $A+B=90^{\circ}$, $B=90^{\circ}-28.0^{\circ}$ Step 12: Solving, $B=62.0^{\circ}$.
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