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: 10

Answer

$x=66.4$ cm $y=60.2$ cm $Y=42.2^{\circ}$

Work Step by Step

Step 1: To find $x$, we use the formula $\sin\theta=\frac{x}{z}$. Step 2: $\sin47.8^{\circ}=\frac{x}{89.6}$ Step 3: $x=89.6\times\sin47.8^{\circ}$ Step 4: Using a calculator, $x\approx66.37$ Step 5: Rounding the answer to three significant degrees, $x\approx66.4$ cm. Step 6: To find $y$, we use the formula $\cos\theta=\frac{y}{z}$. Step 7: $\cos47.8^{\circ}=\frac{y}{89.6}$ Step 8: $y=89.6\times\cos47.8^{\circ}$ Step 9: Using a calculator, $y\approx60.19$ Step 10: Rounding the answer to three significant degrees, $y\approx60.2$ cm. Step 11: As $X+Y=90^{\circ}$, $Y=90^{\circ}-47.8^{\circ}$ Step 12: Solving, $Y=42.2^{\circ}$.
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