Chapter 8: Q. 21 (page 535)

Solve each triangle.
$a = 3, c = 2, B = 110 °$

Short Answer

Expert verified

The solution is $b \approx 4.1, A \approx 42.4 °, C \approx 27.6 °$ .

Step by step solution

Step 1. Given information

$a = 3, c = 2, B = 110 °$

Step 2. Calculation

Use Law of Cosines -

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

$= 9 + 4 - 2 \times 3 \times 2 \cos 110 °$

$= 13 - 12 \times (- 0.34)$

$b \approx 4.1$

For $C$ :

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

localid="1646894339823" role="math" $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \approx \frac{9 + 16.81 - 4}{2 \times 3 \times 4.1} \approx \frac{21.81}{24.6}$

$C \approx \cos^{- 1} \frac{21.81}{24.6} \approx 27.6 °$

Since we know $B$ and $C$ ,

$A = 180 ° - 110 ° - 27.6 ° \approx 42.4 °$

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Solve each triangle.
$a = 3, c = 2, B = 110 °$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Solve each triangle.a=3,c=2,B=110°

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Statistics

Applied Mathematics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each triangle.
$a = 3, c = 2, B = 110 °$