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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. 10 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is $a = 2.05, B = 24.49 掳, C = 125.51 掳$

Step by step solution

01

Step1. Given information

The figure is

02

Step2. Formula used

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

03

Step3. Calculation

$w e h a v e, b = 3, c = 4 a n d, A = 30 掳 w e k n o w, a^{2} = b^{2} + c^{2} - 2 b c . \cos A = 3^{2} + 4^{2} - 2.3.4 . \cos 30 掳 = 9 + 16 - 24 . \frac{\sqrt{3}}{2} = 25 - 12 \sqrt{3} = 25 - 12 脳 1.73 = 25 - 20.76 = 4.24 a = \sqrt{4.24} = 2.05 A g a i n, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{{(2.05)}^{2} + 4^{2} - 3^{2}}{2 . (2.05) . 3} = \frac{4.2025 + 16 - 9}{12.3} = \frac{11.2025}{12.3} = . 91 B = \cos^{- 1} (. 91) = 24.49 掳 A g a i n, w e k n o w A + B + C = 180 掳 30 掳 + 24.49 掳 + C = 180 掳 C = 180 掳 - 54.49 = 125.51 掳$

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$B = 35 掳, C = 65 掳, a = 15$

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