Chapter 8: Q. 18 (page 535)

Solve the triangle
a = 2, c = 1, B = 10 $°$

Short Answer

Expert verified

The solution is

$b = 1.04, A = 156.92 °, C = 13.08 °$

Step by step solution

Step1. Given information

a = 2, c = 1, B = 10 $°$

Step2. Formula used

$b^{2} = a^{2} + c^{2} - 2 a c . \cos B, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}$

Step3. Calculation

We know

$b^{2} = a^{2} + c^{2} - 2 a c . \cos B = 2^{2} + 1^{2} - 2.2.1 . \cos 10 ° = 4 + 1 - 4 . (. 98) = 5 - 3.92 = 1.08 b = \sqrt{1.08} = 1.04 A g a i n, c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{{(1.04)}^{2} + 1^{2} - 2^{2}}{2 . (1.04) . 1} = \frac{1.08 + 1 - 4}{2.08} = \frac{- 1.92}{2.08} = - . 92 A = \cos^{- 1} (- . 92) = 156.92 A g a i n w e k n o w A + B + C = 180 ° 156.92 ° + 10 ° + C = 180 ° C = 180 ° - 166.92 C = 13.08 °$

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 the triangle
a = 2, c = 1, B = 10 $°$

Short Answer

Step by step solution

Step1. Given information

Step2. Formula used

Step3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Logic and Functions

Decision Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Solve the trianglea = 2, c = 1, B = 10°

Short Answer

Step by step solution

Step1. Given information

Step2. Formula used

Step3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Logic and Functions

Decision Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Solve the triangle
a = 2, c = 1, B = 10 $°$