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Chapter 8: Q. 20 (page 535)

Solve each triangle.
$a = 6 b = 4, C = 60 °$

Short Answer

Expert verified

The solution is $c \approx 5.3, A \approx 79 °, B \approx 41 °$ .

Step by step solution

01

Step 1. Given information

$a = 6 b = 4, C = 60 °$

02

Step 2. Calculation

Use Law of Cosines -

$c^{2} = a^{2} + b^{2} - 2 a b \cos C$

$= 36 + 16 - 2 \times 6 \times 4 \cos 60 °$

$\approx 52 - 48 \times 0.5$

$c \approx 5.3$

For $A$ :

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

localid="1646893293730" $\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \approx \frac{16 + 28.09 - 36}{2 \times 4 \times 5.3} \approx \frac{8.09}{42.4}$

$A \approx \cos^{- 1} \frac{8.09}{42.4} \approx 79 °$

Since we know $A$ and $C$ -

$B \approx 180 ° - 60 ° - 79 ° \approx 41 °$

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Most popular questions from this chapter

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