Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Review Exercises - Page 346: 54

Answer

Both sides of the equation in Mollweide's formula are equal, which verifies the accuracy of the information given in the question.

Work Step by Step

$a = 7$ $b = 7\sqrt{3}$ $c = 14$ $A = 30^{\circ}$ $B = 60^{\circ}$ $C = 90^{\circ}$ We can find the value of the left side of Mollweide's formula: $\frac{a-b}{c} = \frac{7-7\sqrt{3}}{14} = -0.366$ We can find the value of the right side of Mollweide's formula: $\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = \frac{sin~\frac{1}{2}(30^{\circ}-60^{\circ})}{cos~\frac{1}{2}90^{\circ}}$ $\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = \frac{sin~\frac{1}{2}(-30^{\circ})}{cos~45^{\circ}}$ $\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = \frac{sin~(-15^{\circ})}{cos~45^{\circ}}$ $\frac{sin~\frac{1}{2}(A-B)}{cos~\frac{1}{2}C} = -0.366$ Both sides of the equation in Mollweide's formula are equal, which verifies the accuracy of the information given in the question.
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