Textbook Question
In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.
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Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 4, Problem 1
In oblique triangle ABC, A = 34°, B = 68°, and a = 4.8. Find b to the nearest tenth.
Verified step by step guidance1
Identify the given information: angle A = 34°, angle B = 68°, and side a = 4.8 opposite angle A.
Calculate the third angle C using the triangle angle sum property: \(C = 180^\circ - A - B\).
Use the Law of Sines to relate sides and angles: \(\frac{a}{\sin A} = \frac{b}{\sin B}\).
Rearrange the Law of Sines formula to solve for side b: \(b = \frac{a \cdot \sin B}{\sin A}\).
Substitute the known values of a, A, and B into the formula and prepare to calculate b (do not compute the final value).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Sum Property of a Triangle
The sum of the interior angles in any triangle is always 180°. Knowing two angles allows you to find the third by subtracting their sum from 180°, which is essential for solving oblique triangles.
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Sum and Difference of Tangent
Law of Sines
The Law of Sines relates the sides and angles of a triangle: (a/sin A) = (b/sin B) = (c/sin C). It is used to find unknown sides or angles in oblique triangles when given some combination of sides and angles.
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4:27Intro to Law of Sines
Rounding and Approximation
When solving trigonometric problems, especially with decimals, rounding to a specified precision (here, the nearest tenth) is important for clarity and practical use. This involves using appropriate significant figures after calculation.
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4:45How to Use a Calculator for Trig Functions
Related Practice
Textbook Question
In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 3i + j, w = i + 3j
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Textbook Question
Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference.sin 6x sin 2x
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Textbook Question
Use the following conditions to solve Exercises 1–4:4 𝝅sin α = ----- , ------- < α < 𝝅5 25 𝝅cos β = ------ , 0 < β < ------13 2Find the exact value of each of the following.cos (α + β)
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Textbook Question
In Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.
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