Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 16.1, Problem 19WE
To determine

To solve: the given triangle.

Expert Solution & Answer
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Answer to Problem 19WE

The given triangle c=7.56,A=44.3°,andB=86.7° .

Explanation of Solution

Given information:

Give lengths to three significant digits and angle measures to the nearest tenth of a degree.

  a=7,b=10,c=49°

Calculation:

Summarize the information in a figure.

  Algebra and Trigonometry: Structure and Method, Book 2, Chapter 16.1, Problem 19WE

Since two sides and the included angle are known, the triangle is as an SAS triangle.

Use the law of cosine to find a .

  c2=a2+b22abcosC

Substitute 10 for b , 7 for a and 49° for C , and simplify

  c2=72+1022(7)(10)cos49°=49+100140cos49°57.15

Take the positive square root on both the sides.

  c257.15c7.56

Next, to find the angles.

Let us find angle B using the law of sines.

  sinBb=sinCcorsinB=bsinCc

Substitute 10 for b , 7.56 for c and 49° for C , and simplify

  sinB=10sin49°7.56=0.5629

Use the inverse sine function to find B .

  Bsin10.998386.7°

The sum of all the angles on a triangle is 180° .

Subtract 49° and 86.7° from 180° to find A ,

  180°86.7°49°=44.3°

Therefore, for the given triangle c=7.56,A=44.3°,andB=86.7° .

Chapter 16 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 16.1 - Prob. 11OECh. 16.1 - Prob. 12OECh. 16.1 - Prob. 13OECh. 16.1 - Prob. 14OECh. 16.1 - Prob. 15OECh. 16.1 - Prob. 16OECh. 16.1 - Prob. 17OECh. 16.1 - Prob. 18OECh. 16.1 - Prob. 1WECh. 16.1 - Prob. 2WECh. 16.1 - Prob. 3WECh. 16.1 - Prob. 4WECh. 16.1 - Prob. 5WECh. 16.1 - Prob. 6WECh. 16.1 - Prob. 7WECh. 16.1 - Prob. 8WECh. 16.1 - Prob. 9WECh. 16.1 - Prob. 10WECh. 16.1 - Prob. 11WECh. 16.1 - Prob. 12WECh. 16.1 - Prob. 13WECh. 16.1 - Prob. 14WECh. 16.1 - Prob. 15WECh. 16.1 - Prob. 16WECh. 16.1 - Prob. 17WECh. 16.1 - Prob. 18WECh. 16.1 - Prob. 19WECh. 16.1 - Prob. 20WECh. 16.1 - Prob. 21WECh. 16.1 - Prob. 22WECh. 16.1 - Prob. 1MRECh. 16.1 - Prob. 2MRECh. 16.1 - Prob. 3MRECh. 16.1 - Prob. 4MRECh. 16.1 - Prob. 5MRECh. 16.1 - Prob. 6MRECh. 16.1 - Prob. 7MRECh. 16.1 - Prob. 8MRECh. 16.2 - Prob. 1OECh. 16.2 - Prob. 2OECh. 16.2 - Prob. 3OECh. 16.2 - Prob. 4OECh. 16.2 - Prob. 5OECh. 16.2 - Prob. 6OECh. 16.2 - Prob. 7OECh. 16.2 - Prob. 8OECh. 16.2 - Prob. 9OECh. 16.2 - Prob. 10OECh. 16.2 - 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Prob. 3WECh. 16.3 - Prob. 4WECh. 16.3 - Prob. 5WECh. 16.3 - Prob. 6WECh. 16.3 - Prob. 7WECh. 16.3 - Prob. 8WECh. 16.3 - Prob. 9WECh. 16.3 - Prob. 10WECh. 16.3 - Prob. 11WECh. 16.3 - Prob. 12WECh. 16.3 - Prob. 13WECh. 16.3 - Prob. 14WECh. 16.3 - Prob. 15WECh. 16.3 - Prob. 16WECh. 16.3 - Prob. 17WECh. 16.3 - Prob. 18WECh. 16.3 - Prob. 19WECh. 16.3 - Prob. 20WECh. 16.3 - Prob. 21WECh. 16.3 - Prob. 22WECh. 16.3 - Prob. 23WECh. 16.3 - Prob. 24WECh. 16.3 - Prob. 25WECh. 16.3 - Prob. 26WECh. 16.3 - Prob. 27WECh. 16.3 - Prob. 28WECh. 16.3 - Prob. 29WECh. 16.3 - Prob. 30WECh. 16.3 - Prob. 1MRECh. 16.3 - Prob. 2MRECh. 16.3 - Prob. 3MRECh. 16.3 - Prob. 4MRECh. 16.3 - Prob. 5MRECh. 16.3 - Prob. 6MRECh. 16.3 - Prob. 7MRECh. 16.3 - Prob. 8MRECh. 16.3 - Prob. 9MRECh. 16.4 - Prob. 1OECh. 16.4 - Prob. 2OECh. 16.4 - Prob. 3OECh. 16.4 - Prob. 4OECh. 16.4 - Prob. 1WECh. 16.4 - Prob. 2WECh. 16.4 - Prob. 3WECh. 16.4 - Prob. 4WECh. 16.4 - Prob. 5WECh. 16.4 - Prob. 6WECh. 16.4 - Prob. 7WECh. 16.4 - Prob. 8WECh. 16.4 - Prob. 9WECh. 16.4 - Prob. 10WECh. 16.4 - Prob. 11WECh. 16.4 - Prob. 12WECh. 16.4 - Prob. 13WECh. 16.4 - Prob. 14WECh. 16.4 - Prob. 15WECh. 16.4 - Prob. 16WECh. 16.4 - Prob. 17WECh. 16.4 - Prob. 18WECh. 16.4 - Prob. 1STCh. 16.4 - Prob. 2STCh. 16.4 - Prob. 3STCh. 16.4 - Prob. 4STCh. 16.4 - Prob. 5STCh. 16.4 - Prob. 6STCh. 16.4 - Prob. 7STCh. 16.4 - Prob. 8STCh. 16.4 - Prob. 9STCh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.5 - Prob. 1OECh. 16.5 - Prob. 2OECh. 16.5 - Prob. 3OECh. 16.5 - Prob. 4OECh. 16.5 - Prob. 5OECh. 16.5 - Prob. 6OECh. 16.5 - Prob. 7OECh. 16.5 - Prob. 8OECh. 16.5 - Prob. 1WECh. 16.5 - Prob. 2WECh. 16.5 - Prob. 3WECh. 16.5 - Prob. 4WECh. 16.5 - Prob. 5WECh. 16.5 - Prob. 6WECh. 16.5 - Prob. 7WECh. 16.5 - Prob. 8WECh. 16.5 - Prob. 9WECh. 16.5 - Prob. 10WECh. 16.5 - Prob. 11WECh. 16.5 - Prob. 12WECh. 16.5 - Prob. 13WECh. 16.5 - Prob. 14WECh. 16.5 - Prob. 15WECh. 16.5 - Prob. 16WECh. 16.5 - Prob. 17WECh. 16.5 - Prob. 18WECh. 16.5 - Prob. 19WECh. 16.5 - Prob. 20WECh. 16.5 - Prob. 1MRECh. 16.5 - Prob. 2MRECh. 16.5 - Prob. 3MRECh. 16.5 - Prob. 4MRECh. 16.5 - Prob. 5MRECh. 16.5 - Prob. 6MRECh. 16.5 - Prob. 7MRECh. 16.5 - Prob. 8MRECh. 16.5 - Prob. 9MRECh. 16.6 - Prob. 1OECh. 16.6 - Prob. 2OECh. 16.6 - Prob. 3OECh. 16.6 - Prob. 4OECh. 16.6 - Prob. 5OECh. 16.6 - Prob. 6OECh. 16.6 - Prob. 7OECh. 16.6 - Prob. 8OECh. 16.6 - Prob. 9OECh. 16.6 - Prob. 10OECh. 16.6 - Prob. 11OECh. 16.6 - Prob. 12OECh. 16.6 - Prob. 13OECh. 16.6 - Prob. 1WECh. 16.6 - Prob. 2WECh. 16.6 - Prob. 3WECh. 16.6 - Prob. 4WECh. 16.6 - Prob. 5WECh. 16.6 - Prob. 6WECh. 16.6 - Prob. 7WECh. 16.6 - Prob. 8WECh. 16.6 - Prob. 9WECh. 16.6 - Prob. 10WECh. 16.6 - Prob. 11WECh. 16.6 - Prob. 12WECh. 16.6 - Prob. 13WECh. 16.6 - Prob. 14WECh. 16.6 - Prob. 15WECh. 16.6 - Prob. 16WECh. 16.6 - Prob. 17WECh. 16.6 - Prob. 18WECh. 16.6 - Prob. 19WECh. 16.6 - Prob. 20WECh. 16.6 - Prob. 1STCh. 16.6 - Prob. 2STCh. 16.6 - Prob. 3STCh. 16.6 - Prob. 4STCh. 16.7 - Prob. 1OECh. 16.7 - Prob. 2OECh. 16.7 - Prob. 3OECh. 16.7 - Prob. 4OECh. 16.7 - Prob. 5OECh. 16.7 - Prob. 6OECh. 16.7 - Prob. 1WECh. 16.7 - Prob. 2WECh. 16.7 - Prob. 3WECh. 16.7 - Prob. 4WECh. 16.7 - Prob. 5WECh. 16.7 - Prob. 6WECh. 16.7 - Prob. 7WECh. 16.7 - Prob. 8WECh. 16.7 - Prob. 9WECh. 16.7 - Prob. 10WECh. 16.7 - Prob. 11WECh. 16.7 - Prob. 12WECh. 16.7 - Prob. 13WECh. 16.7 - Prob. 14WECh. 16.7 - Prob. 15WECh. 16.7 - Prob. 16WECh. 16.7 - Prob. 17WECh. 16.7 - Prob. 18WECh. 16.7 - Prob. 19WECh. 16.7 - Prob. 1MRECh. 16.7 - Prob. 2MRECh. 16.7 - Prob. 3MRECh. 16.7 - Prob. 4MRECh. 16.7 - Prob. 5MRECh. 16.7 - Prob. 6MRECh. 16.8 - Prob. 1OECh. 16.8 - Prob. 2OECh. 16.8 - Prob. 3OECh. 16.8 - Prob. 4OECh. 16.8 - Prob. 1WECh. 16.8 - Prob. 2WECh. 16.8 - Prob. 3WECh. 16.8 - Prob. 4WECh. 16.8 - Prob. 5WECh. 16.8 - Prob. 6WECh. 16.8 - Prob. 7WECh. 16.8 - Prob. 8WECh. 16.8 - Prob. 9WECh. 16.8 - Prob. 10WECh. 16.8 - Prob. 11WECh. 16.8 - Prob. 12WECh. 16.8 - Prob. 13WECh. 16.8 - Prob. 14WECh. 16.8 - Prob. 15WECh. 16.9 - Prob. 1OECh. 16.9 - Prob. 2OECh. 16.9 - Prob. 3OECh. 16.9 - Prob. 4OECh. 16.9 - Prob. 5OECh. 16.9 - Prob. 6OECh. 16.9 - Prob. 7OECh. 16.9 - Prob. 8OECh. 16.9 - Prob. 9OECh. 16.9 - Prob. 10OECh. 16.9 - Prob. 11OECh. 16.9 - Prob. 12OECh. 16.9 - Prob. 13OECh. 16.9 - Prob. 14OECh. 16.9 - Prob. 15OECh. 16.9 - Prob. 16OECh. 16.9 - Prob. 1WECh. 16.9 - Prob. 2WECh. 16.9 - Prob. 3WECh. 16.9 - Prob. 4WECh. 16.9 - Prob. 5WECh. 16.9 - Prob. 6WECh. 16.9 - Prob. 7WECh. 16.9 - Prob. 8WECh. 16.9 - Prob. 9WECh. 16.9 - Prob. 10WECh. 16.9 - Prob. 11WECh. 16.9 - Prob. 12WECh. 16.9 - Prob. 13WECh. 16.9 - Prob. 14WECh. 16.9 - Prob. 15WECh. 16.9 - Prob. 16WECh. 16.9 - Prob. 17WECh. 16.9 - Prob. 18WECh. 16.9 - Prob. 19WECh. 16.9 - Prob. 1MRECh. 16.9 - Prob. 2MRECh. 16.9 - Prob. 3MRECh. 16.9 - Prob. 4MRECh. 16.9 - Prob. 5MRECh. 16.9 - Prob. 6MRECh. 16.9 - Prob. 7MRECh. 16.9 - Prob. 1STCh. 16.9 - Prob. 2STCh. 16.9 - Prob. 3STCh. 16 - Prob. 1CRCh. 16 - Prob. 2CRCh. 16 - Prob. 3CRCh. 16 - Prob. 4CRCh. 16 - Prob. 5CRCh. 16 - Prob. 6CRCh. 16 - Prob. 7CRCh. 16 - Prob. 8CRCh. 16 - Prob. 9CRCh. 16 - Prob. 10CRCh. 16 - Prob. 1CTCh. 16 - Prob. 2CTCh. 16 - Prob. 3CTCh. 16 - Prob. 4CTCh. 16 - Prob. 5CTCh. 16 - Prob. 6CTCh. 16 - Prob. 7CTCh. 16 - Prob. 8CTCh. 16 - Prob. 9CTCh. 16 - Prob. 10CTCh. 16 - Prob. 11CTCh. 16 - Prob. 12CTCh. 16 - Prob. 13CTCh. 16 - Prob. 14CTCh. 16 - Prob. 15CT
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