Domanda del libro di testo
Starting at point A, a ship sails 18.5 km on a bearing of 189°, then turns and sails 47.8 km on a bearing of 317°. Find the distance of the ship from point A.
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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 48
Find the area of each triangle using the formula 𝓐 = ½ bh, and then verify that the formula 𝓐 = ½ ab sin C gives the same result.
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Guida verificata passo dopo passo1
Identify the base (b) and the height (h) of the triangle from the given image or information. The base is one side of the triangle, and the height is the perpendicular distance from the opposite vertex to this base.
Use the formula for the area of a triangle based on base and height: \(\mathcal{A} = \frac{1}{2} b h\). Substitute the values of base and height into this formula to express the area.
Next, identify two sides of the triangle, say \(a\) and \(b\), and the included angle \(C\) between them from the image or given data.
Use the formula for the area of a triangle using two sides and the included angle: \(\mathcal{A} = \frac{1}{2} a b \sin C\). Substitute the values of sides \(a\), \(b\), and angle \(C\) into this formula.
Compare the two expressions for the area obtained from the two formulas to verify that they give the same result, confirming the consistency of the area calculation methods.
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Area of a Triangle Using Base and Height
The formula 𝓐 = ½ bh calculates the area of a triangle by multiplying the base length (b) by the height (h) perpendicular to that base, then dividing by two. This method requires knowing the height, which is the perpendicular distance from the base to the opposite vertex.
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Percorso guidato
4:02
Calculating Area of SAS Triangles
Area of a Triangle Using Two Sides and Included Angle
The formula 𝓐 = ½ ab sin C finds the area by using two sides (a and b) and the sine of the included angle (C) between them. This approach is useful when the height is not known but two sides and the included angle are given, leveraging trigonometric relationships.
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Percorso guidato
4:02Calculating Area of SAS Triangles
Relationship Between the Two Area Formulas
Both formulas calculate the same area but use different known elements: one uses base and height, the other uses two sides and the included angle. Verifying equality involves understanding that height can be expressed as b sin C, linking the two methods through trigonometry.
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Percorso guidato
4:30Calculating Area of ASA Triangles
Pratica correlata
Domanda del libro di testo
A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310°. A wind of 37 mph is blowing from a bearing of 212°. In what direction should the pilot fly, and what will be her ground speed?
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Domanda del libro di testo
Starting at point X, a ship sails 15.5 km on a bearing of 200°, then turns and sails 2.4 km on a bearing of 320°. Find the distance of the ship from point X.
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Domanda del libro di testo
One boat pulls a barge with a force of 100 newtons. Another boat pulls the barge at an angle of 45° to the first force, with a force of 200 newtons. Find the resultant force acting on the barge, to the nearest unit, and the angle between the resultant and the first boat, to the nearest tenth.
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Domanda del libro di testo
Write each vector in the form a i + b j.
〈2, 0〉
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Domanda del libro di testo
Solve each problem. See Examples 5 and 6.
Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.
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