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: 11

Answer

$n=154$ m $p= 198$ m $M=38.8^{\circ}$

Work Step by Step

Step 1: To find $n$, we use the formula $\tan\theta=\frac{n}{m}$. Step 2: $\tan51.2^{\circ}=\frac{n}{124}$ Step 3: $n=124\times\tan51.2^{\circ}$ Step 4: Using a calculator, $n\approx154.2$ Step 5: Rounding the answer to three significant degrees, $n\approx154$ m. Step 6: To find $p$, we use the formula $\cos\theta=\frac{m}{p}$. Step 7: $\cos51.2^{\circ}=\frac{124}{p}$ Step 8: $p=\frac{124}{\cos51.2^{\circ}}$ Step 9: Using a calculator, $p\approx197.9$ Step 10: Rounding the answer to three significant degrees, $p\approx198$ m. Step 11: As $M+N=90^{\circ}$, $M=90^{\circ}-51.2^{\circ}$ Step 12: Solving, $M=38.8^{\circ}$.
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