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Chapter 8: Q. 25 (page 535)

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

Short Answer

Expert verified

The solution is $A \approx 67.4 °, B = 90 °, C \approx 22.6 °$ .

Step by step solution

01

Step 1. Given information

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

02

Step 2. Calculation

For A:

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

$A = \cos^{- 1} \frac{5}{13} \approx 67.4 °$

For $B$ :

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

$B = \cos^{- 1} (0) = 90 °$

Since we know $A$ and $B$ ,

$C = 180 ° - A - B$

$\approx 180 ° - 67.4 ° - 90 °$

$\approx 22.6 °$

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