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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 13 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is

$A = 48.51 掳, B = 38.62 掳, C = 92.87 掳$

Step by step solution

01

Step1. Given information

02

Step2. Formula used

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$

03

Step3. Calculation

$W e k n o w, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{5^{2} + 8^{2} - 6^{2}}{2.5.8} = \frac{25 + 64 - 36}{80} = \frac{53}{80} = . 6625 A = \cos^{- 1} (. 6625) = 48.51 掳 A g a i n, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{6^{2} + 8^{2} - 5^{2}}{2.6.8} = \frac{36 + 64 - 25}{96} = \frac{75}{96} = . 78125 B = \cos^{- 1} (. 78125) = 38.62 掳 A g a i n, w e k n o w A + B + C = 180 掳 48.51 掳 + 38.62 掳 + C = 180 掳 C = 180 掳 - 87.13 掳 = 92.87 掳$

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