The Ambiguous Case When we are given two sides of a triangle and an angle opposite one of these sides, this is known as the ambiguous case because the known information may result in one triangle, two triangles, or no triangle at all. Suppose that we are given sides a andb and angle A as illustrated in the figure on the left. If ach=bsinA, then a is too short and no triangle is formed. If h
The Ambiguous Case When we are given two sides of a triangle and an angle opposite one of these sides, this is known as the ambiguous case because the known information may result in one triangle, two triangles, or no triangle at all. Suppose that we are given sides a andb and angle A as illustrated in the figure on the left. If ach=bsinA, then a is too short and no triangle is formed. If h
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.CR: Review Exercises
Problem 42CR
Related questions
Question
100%
Transcribed Image Text:7:27
Remove
A
sin A
The Ambiguous Case
When we are given two sides of a triangle and an angle opposite one of these sides,
this is known as the ambiguous case because the known information may result in o
triangle, two triangles, or no triangle at all. Suppose that we are given sides a andb
and angle A as illustrated in the figure on the left.
The Ambiguous Case
2. a 6, b=8, A=35°
Save
If h<a<b, then there are two possible triangles. In
this situation, angle B has two possibilities, one
acute and one obtuse that have the same sine.
But if a b then there is only one triangle again.
3. a = 1, b = 2, A = 50°
4. a = 3,b=2, A = 50°
5. a=4, b=5, A= 60°
If ach=bsinA, then a
is too short and no
triangle is formed.
Determine how many triangles are possible for the information given. If one or two
triangles are possible, find angle B.
1. a 3, b 2, A=40°
6. a = 3,b 7, A=70°
If ah then we have
a right triangle.
Turn In
Copyright © 2023 International Academy of
Science. All Rights Reserved.
h-b sin A
www.acellus.com
X
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 15 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning