Trigonometry (10th Edition)

Published by Pearson

Chapter 2 - Acute Angles and Right Triangles - Section 2.4 Solving Right Triangles - 2.4 Exercises - Page 73: 26

Answer

$b=35.6$ ft $c=45.3$ ft $A=38.3^{\circ}$

Work Step by Step

Step 1: To find $b$, we use the formula $\tan\theta=\frac{b}{a}$. Step 2: $\tan51.7^{\circ}=\frac{b}{28.1}$ Step 3: $b=\tan51.7^{\circ}\times28.1$ Step 4: Using a calculator, $b\approx35.58$ Step 5: Rounding the answer to three significant degrees, $b\approx35.6$ ft. Step 6: To find $c$, we use the formula $\cos\theta=\frac{a}{c}$. Step 7: $\cos51.7^{\circ}=\frac{28.1}{c}$ Step 8: $c=\frac{28.1}{\cos51.7^{\circ}}$ Step 9: Using a calculator, $c\approx45.34$ Step 10: Rounding the answer to three significant degrees, $c\approx45.3$ ft. Step 11: As $A+B=90^{\circ}$, $A=90^{\circ}-51.7^{\circ}$ Step 12: Solving, $A=38.3^{\circ}$.

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