Chapter 8: Q. 22 (page 535)

Solve each triangle.
$b = 4 c = 1, A = 120 °$

Short Answer

Expert verified

The solution is $a \approx 4.6, B \approx 49.3 °, C \approx 10.7 °$

Step by step solution

Step 1. Given information

$b = 4 c = 1, A = 120 °$

Step 2. Calculation

Use Law of Cosines -

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

$= 16 + 1 - 2 \times 4 \times 1 \cos 120 °$

$= 17 - 8 \times - 0.5$

$a \approx 4.6$

For C:

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

localid="1646894986845" $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \approx \frac{21.16 + 16 - 1}{2 \times 4.6 \times 4} \approx \frac{36.16}{36.8}$

$C \approx \cos^{- 1} \frac{36.16}{36.8} \approx 10.7 °$

Since we know A and C,

$B = 180 ° - 120 ° - 10.7 ° \approx 49.3 °$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each triangle.
$b = 4 c = 1, A = 120 °$

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

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Solve each triangle.b=4c=1,A=120°

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

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Solve each triangle.
$b = 4 c = 1, A = 120 °$