Domanda del libro di testo
Find the area of each triangle ABC.
A = 56.80°, b = 32.67 in., c = 52.89 in.
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Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 58
Find the area of each triangle ABC.
A = 59.80°, b = 15.00 cm, C = 53.10°
Guida verificata passo dopo passo1
Identify the given elements of the triangle: angle A = 59.80°, side b = 15.00 cm, and angle C = 53.10°.
Calculate the third angle B using the triangle angle sum property: \(B = 180^\circ - A - C\).
Use the Law of Sines to find side a, which is opposite angle A: \(\frac{a}{\sin A} = \frac{b}{\sin B}\), so \(a = b \times \frac{\sin A}{\sin B}\).
Calculate the height (altitude) of the triangle relative to base b using the formula \(h = a \times \sin C\).
Find the area of the triangle using the formula \(\text{Area} = \frac{1}{2} \times b \times h\).
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Law of Sines
The Law of Sines relates the sides and angles of a triangle, stating that the ratio of a side length to the sine of its opposite angle is constant. It is useful for finding unknown sides or angles when given two angles and one side, as in this problem.
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Percorso guidato
4:27
Intro to Law of Sines
Triangle Angle Sum Property
The sum of the interior angles in any triangle is always 180°. Knowing two angles allows you to find the third angle, which is essential for applying trigonometric formulas correctly.
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Percorso guidato
4:47Sum and Difference of Tangent
Area Formula Using Two Sides and Included Angle
The area of a triangle can be calculated using the formula (1/2)ab sin(C), where a and b are two sides and C is the included angle between them. This formula is especially useful when two sides and the included angle are known or can be found.
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Percorso guidato
4:30Calculating Area of ASA Triangles
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