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Chapter 8: Q. 24 (page 535)

Solve each triangle.
$a = 3, c = 2, B = 90 °$

Short Answer

Expert verified

The solution is $b \approx 3.6, A \approx 56.3 °, C \approx 33.7 °$ .

Step by step solution

01

Step 1. Given information

$a = 3, c = 2, B = 90 °$

02

Step 2. Calculation

Use Law of Cosines -

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

$= 9 + 4 - 2 \times 3 \times 2 \cos 90 °$

$= 13 - 12 \times 0$

$b \approx 3.6$

For C:

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

localid="1646896357731" $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \approx \frac{9 + 12.96 - 4}{2 \times 3 \times 3.6} \approx \frac{17.96}{21.6}$

$C \approx \cos^{- 1} \frac{17.96}{21.6} \approx 33.7 °$

Since we know B and C,

$A = 180 ° - 90 ° - 33.7 ° \approx 56.3 °$

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