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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. 25 (page 535)

Solve each triangle.
$a = 12, b = 13, c = 5$

Short Answer

Expert verified

The solution is $A 鈮� 67.4 掳, B = 90 掳, C 鈮� 22.6 掳$ .

Step by step solution

01

Step 1. Given information

$a = 12, b = 13, c = 5$

02

Step 2. Calculation

For A:

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{169 + 25 - 144}{2 路 13 路 5} = \frac{5}{13}$

$A = \cos^{- 1} \frac{5}{13} 鈮� 67.4 掳$

For $B$ :

$\cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{144 + 25 - 169}{2 路 12 路 5} = \frac{0}{120} = 0$

$B = \cos^{- 1} (0) = 90 掳$

Since we know $A$ and $B$ ,

$C = 180 掳 - A - B$

$鈮� 180 掳 - 67.4 掳 - 90 掳$

$鈮� 22.6 掳$

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Most popular questions from this chapter

Solve each triangle.

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