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Q. 29

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Precalculus Enhanced with Graphing Utilities

Found in: Page 535

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Solve each triangle.
$a = 5, b = 8, c = 9$

The required triangle is

$A = 33.90 ° B = 62.61 ° C = 83.49 °$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

$a = 5, b = 8, c = 9$

To find the angles $A, B, C$

Step 2: Calculation

$F o r A : \cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{8^{2} + 9^{2} - 5^{2}}{2 \times 8 \times 9} = 0.83 A = \cos^{- 1} (0.83) = 33.90 °$

$F o r B : \cos (B) = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{5^{2} + 9^{2} - 8^{2}}{2 \times 5 \times 9} = 0.46 B = \cos^{- 1} (0.46) = 62.61 °$

Since we know A and B

$C = 180 ° - A - B = 180 ° - 33.90 ° - 62.61 ° = 83.49 °$

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