Q. 31 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. 31 (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 $b = 4, c = 6, B = 20 掳$

Short Answer

Expert verified

With the given measurements two triangles are possible.

$F o r 鈻� A_{1} B C_{1,} a_{1} = 4.5, b = 4, c = 6, A_{1} = 129.14 掳, B = 20 掳, C_{1} = 30.86 掳 F o r 鈻� A_{2} B C_{2}, a_{2} = 3.3, b = 4, c = 6, A_{2} = 10.86 掳, B = 20 掳, C_{2} = 149.14 掳$

Step by step solution

Step 1. Given information

$b = 4, c = 6, B = 20 掳$

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

$B y L a w o f S i n e s, F o r C, \frac{鈬� \sin (B)}{b} = \frac{\sin (C)}{c} 鈬� \sin (C) = \frac{\sin (B) 脳 c}{b} = \sin (20 掳) 脳 \frac{6}{4} = 0.342 脳 1.5 = 0.513 C_{1} 鈮� 30.86 掳 o r C_{2} 鈮� 180 掳 - 30.86 掳 = 149.14 掳 S i n c e, C_{1} + B < 180 掳, 鈻� A_{1} B C_{1} i s p o s s i b l e a n d C_{2} + B < 180 掳, 鈻� A_{2} B C_{2} i s p o s s i b l e . I n 鈻� A_{1} B C_{1} : F o r A_{1}, 鈬� A_{1} = 180 掳 - B - C_{1} = 180 掳 - 20 掳 - 30.86 掳 = 180 掳 - 50.86 掳 = 129.14 掳 F o r a_{1}, \frac{鈬� \sin (B)}{b} = \frac{\sin (A_{1})}{a_{1}} 鈬� a_{1} = \frac{\sin (A_{1}) 脳 b}{\sin (B)} = \frac{\sin (129.14 掳) 脳 4}{\sin (20 掳)} = \frac{0.7756 脳 2}{0.342} = \frac{1.5512}{0.342} = 4.535 鈮� 4.5 I n 鈻� A_{2} B C_{2} : F o r A_{2,} 鈬� A_{2} = 180 掳 - 20 掳 - 149.14 掳 = 180 掳 - 169.14 掳 = 10.86 掳 F o r a_{2}, \frac{鈬� \sin (B)}{b} = \frac{\sin (A_{2})}{a_{2}} 鈬� a_{2} = \frac{\sin (A_{2}) 脳 b}{\sin (B)} = \frac{\sin (10.86 掳) 脳 4}{\sin (20 掳)} = \frac{0.1884 脳 4}{0.342} = \frac{1.1354}{0.342} = 3.3198 鈮� 3.3$

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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 $b = 4, c = 6, B = 20 掳$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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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=6,B=20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

Decision Maths

Discrete Mathematics

Pure Maths

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

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 $b = 4, c = 6, B = 20 掳$