Ch. 1 - Trigonometric Functions

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 1 - Trigonometric Functions

Problema 43

Capitolo 2, Problema 43

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

Guida verificata passo dopo passo

Identify the measures of the angles in the triangle. If the problem provides side lengths, use the Law of Cosines to find the angles. The Law of Cosines formula is: \(c^2 = a^2 + b^2 - 2ab \cos(C)\), where \(C\) is the angle opposite side \(c\).

Classify the triangle by its angles: if all angles are less than 90°, it is an acute triangle; if one angle is exactly 90°, it is a right triangle; if one angle is greater than 90°, it is an obtuse triangle.

Classify the triangle by its sides: if all three sides are equal, it is equilateral; if exactly two sides are equal, it is isosceles; if all sides are different lengths, it is scalene.

To verify side equality, compare the given side lengths directly. If only angles are given, use the Law of Sines or Law of Cosines to find side lengths if needed.

Summarize your classification by combining the angle-based and side-based types, for example, 'acute isosceles' or 'right scalene'.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Classification of Triangles by Angles

Triangles are classified based on their angles as acute (all angles less than 90°), right (one angle exactly 90°), or obtuse (one angle greater than 90°). Understanding these categories helps determine the triangle's shape and properties.

Video consigliato:

Percorso guidato

5:35

30-60-90 Triangles

Classification of Triangles by Sides

Triangles are also classified by side lengths: equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different). This classification aids in identifying symmetry and congruence within the triangle.

Video consigliato:

Percorso guidato

4:18

Finding Missing Side Lengths

Relationship Between Triangle Angles and Sides

The type of angles in a triangle influences the relative lengths of its sides, and vice versa. For example, an equilateral triangle is always acute, while an obtuse triangle cannot be equilateral. Recognizing these relationships is key to accurate classification.

Video consigliato:

Percorso guidato

04:33

Find the Angle Between Vectors

Pratica correlata

Domanda del libro di testo

Give all six trigonometric function values for each angle θ . Rationalize denominators when applicable.

sec θ = 5/4 , and θ is in quadrant IV

785

views

Domanda del libro di testo

Perform each calculation. See Example 3. 90° ― 51° 28'

607

views

Domanda del libro di testo

Perform each calculation.

110° 25' + 32° 55'

602

views

rank

Domanda del libro di testo

Perform each calculation. See Example 3. 47° 29' ― 71° 18'

627

views

Domanda del libro di testo

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.

tan θ < 0 , cos θ < 0

1278

views

Domanda del libro di testo

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) III , r/y

565

views