Textbook Question
Which one of the following sets of data does not determine a unique triangle?
a. A = 50°, b = 21, a = 19
b. A = 45°, b = 10, a = 12
c. A = 130°, b = 4, a = 7
d. A = 30°, b = 8, a = 4
Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 8, Problem 1
Fill in the blank(s) to correctly complete each sentence.
A triangle that is not a right triangle is a(n) _________ triangle.
Verified step by step guidance1
Recall the classification of triangles based on their angles: a right triangle has one angle exactly equal to 90 degrees.
Understand that if a triangle does not have a right angle, it means none of its angles is 90 degrees.
Triangles without a right angle can be either acute (all angles less than 90 degrees) or obtuse (one angle greater than 90 degrees).
Therefore, a triangle that is not a right triangle is called an \(\textbf{oblique}\) triangle.
So, the blank should be filled with the word \(\textit{oblique}\) to correctly complete the sentence.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Types of Triangles Based on Angles
Triangles are classified by their angles into acute, right, and obtuse triangles. A right triangle has one 90-degree angle, while acute triangles have all angles less than 90 degrees, and obtuse triangles have one angle greater than 90 degrees.
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30-60-90 Triangles
Right Triangle Definition
A right triangle is defined as a triangle that contains exactly one right angle (90 degrees). This classification is fundamental in trigonometry because many formulas and theorems apply specifically to right triangles.
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5:3530-60-90 Triangles
Non-Right Triangles
Triangles that do not have a right angle are called non-right triangles, which include acute and obtuse triangles. Understanding this distinction helps in applying appropriate trigonometric methods, such as the Law of Sines or Law of Cosines.
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Related Practice
Textbook Question
Use the law of sines to find the indicated part of each triangle ABC.
Find b if C = 74.2°, c = 96.3 m, B = 39.5
Textbook Question
Use the law of sines to find the indicated part of each triangle ABC.
Find B if C = 51.3°, c = 68.3 m, b = 58.2 m
Textbook Question
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
a. two triangles
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Textbook Question
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
b. exactly one triangle
<IMAGE>
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Textbook Question
CONCEPT PREVIEW Assume a triangle ABC has standard labeling.
a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.
b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.
a, b, and C
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