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Ch. 7 - Applications of Trigonometry and Vectors
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. 7 - Applications of Trigonometry and VectorsProblema 34
Capitolo 8, Problema 34

To determine the distance RS across a deep canyon, Rhonda lays off a distance TR = 582 yd. She then finds that T = 32° 50' and R = 102° 20'. Find RS. See the figure.


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1
Identify the triangle involved and label the vertices as T, R, and S, where TR is the known side with length 582 yards, and the angles at T and R are given as 32° 50' and 102° 20' respectively.
Convert the given angles from degrees and minutes to decimal degrees for easier calculation: for example, 32° 50' becomes 32 + 50/60 degrees.
Calculate the third angle at vertex S using the triangle angle sum property: \(\angle S = 180^\circ - \angle T - \angle R\).
Use the Law of Sines to find the length of side RS. The Law of Sines states: \(\frac{RS}{\sin(\angle T)} = \frac{TR}{\sin(\angle S)}\).
Rearrange the Law of Sines formula to solve for RS: \(RS = \frac{TR \times \sin(\angle T)}{\sin(\angle S)}\). Substitute the known values and calculate the sine values to find RS.

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Law of Sines

The Law of Sines relates the sides and angles of any triangle, stating that the ratio of a side length to the sine of its opposite angle is constant. It is essential for finding unknown sides or angles when two angles and one side are known, as in this problem involving triangle measurements.
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Intro to Law of Sines

Angle Measurement and Conversion

Understanding how to interpret and convert angles given in degrees and minutes is crucial. Since angles are provided in degrees and minutes (e.g., 32° 50'), converting them to decimal degrees or radians facilitates calculations using trigonometric functions.
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Reference Angles on the Unit Circle

Triangle Angle Sum Property

The sum of the interior angles of any triangle is always 180°. Knowing two angles allows calculation of the third, which is necessary to apply the Law of Sines correctly and solve for the unknown side RS in the triangle.
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Sum and Difference of Tangent
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