Chapter 8: Q. 19 (page 535)

Solve each triangle.
$b = 1 c = 3, A = 80 °$

Short Answer

Expert verified

The solution is $a \approx 3, B \approx 19.6 °, C \approx 80.4 °$ .

Step by step solution

Step 1. Given information

$b = 1 c = 3, A = 80 °$

Step 2. Calculation

Use Law of Cosines -

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

$= 1 + 9 - 2 \times 1 \times 3 \cos 80 °$

localid="1646858065045" $\approx 10 - (6 \times 0.17)$

localid="1646891425407" $a \approx 3$

For C:

localid="1646858918647" $c^{2} = a^{2} + b^{2} - 2 a b \cos C$

localid="1646891487034" $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \approx \frac{9 + 1 - 9}{2 \times 3 \times 1} \approx \frac{1}{6}$

localid="1646891543751" $C \approx \cos^{- 1} \frac{1}{6} \approx 80.4 °$

Since we know $A$ and $C$ ,

$B \approx 180 ° - 80 ° - 80.4 ° \approx 19.6 °$

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Solve each triangle.
$b = 1 c = 3, A = 80 °$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Solve each triangle.b=1c=3,A=80°

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

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Solve each triangle.
$b = 1 c = 3, A = 80 °$