Q. 28 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. 28 (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
$a = 2, c = 1, A = 120 掳$

Short Answer

Expert verified

It results in one triangle.

The required triangle is $a = 2, c = 1, A = 120 掳, b = 1.31, B = 34.53 掳, C = 25.47 掳$

Step by step solution

Given information

$a = 2, c = 1, A = 120 掳$

Calculation

$B y L a w o f S i n e s, \frac{\sin A}{a} = \frac{\sin C}{c} \frac{\sin 120}{2} = \frac{\sin C}{1} \sin C = \frac{\sin 120}{2} = 0.43$

$T h e r e a r e t w o a n g l e s C, 0 掳 < C < 180 掳, f o r w h i c h \sin C 鈮� 0.43 C 1 鈮� 25.47 掳 a n d C 2 鈮� 154.53 掳 T h e s e c o n d p o s s i b i l i t y C 2 鈮� 154.53 掳, i s r u l e d o u t b e c a u s e A = 120 掳 m a k e s A + C 2 = 274.53 掳 > 180 掳 N o w u \sin g C 1 = 25.47 掳, w e f i n d B = 180 掳 - A - C 1 = 180 - 120 - 25.47 = 34.53 掳 T h e t h i r d s i d e a, m a y n o w b e d e t e r m i n e d u \sin g L a w o f S i n e s \frac{\sin A}{a} = \frac{\sin B}{b} \frac{\sin 120}{2} = \frac{\sin 34.53}{b} b = 1.31$

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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
$a = 2, c = 1, A = 120 掳$

Short Answer

Step by step solution

Given information

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 resultsa=2,c=1,A=120掳

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Calculus

Discrete Mathematics

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
$a = 2, c = 1, A = 120 掳$