Skip to main content
Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 1 - Trigonometric FunctionsProblema 39
Capitolo 2, Problema 39

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
1
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 categories, 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:
1m

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 into 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 as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different). This classification provides insight into the triangle's symmetry and side relationships.
Video consigliato:
Percorso guidato
4:18
Finding Missing Side Lengths

Relationship Between Angles and Sides in Triangles

The size of a triangle's angles is related to the lengths of its sides: larger sides face larger angles. This principle helps in identifying the triangle type when given side lengths or angles, aiding in accurate classification.
Video consigliato:
Percorso guidato
04:33
Find the Angle Between Vectors
Pratica correlata
Domanda del libro di testo

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3. cos θ > 0 , sec θ > 0

1176
views
Domanda del libro di testo

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

cos θ = ―5/8 , and θ is in quadrant III

938
views
Domanda del libro di testo

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.

―345°

742
views
Domanda del libro di testo

Find the measure of the smaller angle formed by the hands of a clock at the following times. 8:20

712
views
Domanda del libro di testo

Perform each calculation. See Example 3. 75° 15' + 83° 32'

548
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.) II , y/x

555
views