Q. 36 Two sides and an angle are given... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 36 (page 528)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results $b = 4, c = 5, B = 40 掳$

Short Answer

Expert verified

With the given measurements two triangles are possible.

$F o r 鈻� A_{1} B C_{1,} a_{1} = 6.2, b = 4, c = 5, A_{1} = 86.55 掳, B = 40 掳, C_{1} = 53.45 掳 F o r 鈻� A_{2} B C_{2}, a_{2} = 1.4, b = 4, c = 5, A_{2} = 13.45 掳, B = 40 掳, C_{2} = 126.55 掳$

Step by step solution

Step 1. Given information

$b = 4, c = 5, B = 40 掳$

For a triangle with sides a, b, c and opposite angles A, B, C, respectively, Law of sines is given as:

$\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}$

Step 2. Calculation

$B y L a w o f S i n e s, F o r C, \frac{鈬� \sin (B)}{b} = \frac{\sin (C)}{c} 鈬� \sin (C) = \frac{\sin (B) 脳 c}{b} = \sin (40 掳) 脳 \frac{5}{4} = 0.6427 脳 1.25 = 0.803375 C_{1} 鈮� 53.45 掳 o r C_{2} 鈮� 180 掳 - 53.45 掳 = 126.55 掳 S i n c e, C_{1} + B < 180 掳, 鈻� A_{1} B C_{1} i s p o s s i b l e a n d C_{2} + B < 180 掳, 鈻� A_{2} B C_{2} i s p o s s i b l e . I n 鈻� A_{1} B C_{1} : F o r A_{1}, 鈬� A_{1} = 180 掳 - B - C_{1} = 180 掳 - 40 掳 - 53.45 掳 = 180 掳 - 93.45 掳 = 86.55 掳 F o r a_{1}, \frac{鈬� \sin (B)}{b} = \frac{\sin (A_{1})}{a_{1}} 鈬� a_{1} = \frac{\sin (A_{1}) 脳 b}{\sin (B)} = \frac{\sin (86.55 掳) 脳 4}{\sin (40 掳)} = \frac{0.9981 脳 4}{0.6427} = \frac{3.9924}{0.6427} = 6.2 I n 鈻� A_{2} B C_{2} : F o r A_{2,} 鈬� A_{2} = 180 掳 - 40 掳 - 126.55 掳 = 180 掳 - 166.55 掳 = 13.45 掳 F o r a_{2}, \frac{鈬� \sin (B)}{b} = \frac{\sin (A_{2})}{a_{2}} 鈬� a_{2} = \frac{\sin (A_{2}) 脳 b}{\sin (B)} = \frac{\sin (13.45 掳) 脳 4}{\sin (40 掳)} = \frac{0.2325 脳 4}{0.6427} = \frac{0.93}{0.6427} = 1.447 鈮� 1.4$

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results $b = 4, c = 5, B = 40 掳$

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

Geometry

Decision Maths

Discrete Mathematics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that resultsb=4,c=5,B=40掳

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

Geometry

Decision Maths

Discrete Mathematics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results $b = 4, c = 5, B = 40 掳$