McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 8.6, Problem 22WE
To determine

To find: the length of diagonal AC¯ .

Expert Solution & Answer
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Answer to Problem 22WE

The length of diagonal AC is about 9 cm.

Explanation of Solution

Given Information:

Points A,B and C are three consecutive vertices of a regular decagon., whose sides are 16 cm long.

Calculation:

Consider the figure,

  McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 8.6, Problem 22WE

Three useful trigonometric ratios, given below in abbreviated form,

  tanA=oppositeAdjacentsinA=oppositeHypotenusecosA=AdjacentHypotenuse

Angle in regular polygon of n sides is given by,

  360°n=36°

In case of diagram, number of sides is 10. Therefore, angle in regular decagon is given by

  360°10=36°

Apply the sine formula in the right angle triangle for calculating length,

  sinC=AC16

Put the value of angle, to get

  sin36°=AC16

Use cross-multiplication, to get

  AC=16sin36°

Use, the table of sine of angle provided, the approximate value of AC is calculated as,

  AC=16×0.587AC9cm

Therefore, the length of diagonal AC is about 9 cm.

Chapter 8 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 8.1 - Prob. 11CECh. 8.1 - Prob. 12CECh. 8.1 - Prob. 13CECh. 8.1 - Prob. 14CECh. 8.1 - Prob. 15CECh. 8.1 - Prob. 16CECh. 8.1 - Prob. 17CECh. 8.1 - Prob. 1WECh. 8.1 - Prob. 2WECh. 8.1 - Prob. 3WECh. 8.1 - Prob. 4WECh. 8.1 - Prob. 5WECh. 8.1 - Prob. 6WECh. 8.1 - Prob. 7WECh. 8.1 - Prob. 8WECh. 8.1 - Prob. 9WECh. 8.1 - Prob. 10WECh. 8.1 - Prob. 11WECh. 8.1 - Prob. 12WECh. 8.1 - Prob. 13WECh. 8.1 - Prob. 14WECh. 8.1 - Prob. 15WECh. 8.1 - Prob. 16WECh. 8.1 - Prob. 17WECh. 8.1 - Prob. 18WECh. 8.1 - Prob. 19WECh. 8.1 - Prob. 20WECh. 8.1 - Prob. 21WECh. 8.1 - Prob. 22WECh. 8.1 - Prob. 23WECh. 8.1 - Prob. 24WECh. 8.1 - Prob. 25WECh. 8.1 - Prob. 26WECh. 8.1 - Prob. 27WECh. 8.1 - Prob. 28WECh. 8.1 - Prob. 29WECh. 8.1 - Prob. 30WECh. 8.1 - Prob. 31WECh. 8.1 - Prob. 32WECh. 8.1 - Prob. 33WECh. 8.1 - Prob. 34WECh. 8.1 - Prob. 35WECh. 8.1 - Prob. 36WECh. 8.1 - Prob. 37WECh. 8.1 - Prob. 38WECh. 8.1 - Prob. 39WECh. 8.1 - Prob. 40WECh. 8.1 - Prob. 41WECh. 8.1 - Prob. 42WECh. 8.1 - Prob. 43WECh. 8.1 - Prob. 44WECh. 8.1 - Prob. 45WECh. 8.2 - Prob. 1CECh. 8.2 - Prob. 2CECh. 8.2 - Prob. 3CECh. 8.2 - Prob. 4CECh. 8.2 - Prob. 5CECh. 8.2 - Prob. 6CECh. 8.2 - Prob. 7CECh. 8.2 - Prob. 8CECh. 8.2 - Prob. 9CECh. 8.2 - Prob. 10CECh. 8.2 - Prob. 11CECh. 8.2 - Prob. 12CECh. 8.2 - Prob. 13CECh. 8.2 - Prob. 14CECh. 8.2 - Prob. 15CECh. 8.2 - Prob. 16CECh. 8.2 - Prob. 17CECh. 8.2 - Prob. 18CECh. 8.2 - Prob. 1WECh. 8.2 - Prob. 2WECh. 8.2 - Prob. 3WECh. 8.2 - Prob. 4WECh. 8.2 - Prob. 5WECh. 8.2 - Prob. 6WECh. 8.2 - Prob. 7WECh. 8.2 - Prob. 8WECh. 8.2 - Prob. 9WECh. 8.2 - Prob. 10WECh. 8.2 - Prob. 11WECh. 8.2 - Prob. 12WECh. 8.2 - Prob. 13WECh. 8.2 - Prob. 14WECh. 8.2 - Prob. 15WECh. 8.2 - Prob. 16WECh. 8.2 - Prob. 17WECh. 8.2 - Prob. 18WECh. 8.2 - Prob. 19WECh. 8.2 - Prob. 20WECh. 8.2 - Prob. 21WECh. 8.2 - Prob. 22WECh. 8.2 - Prob. 23WECh. 8.2 - Prob. 24WECh. 8.2 - Prob. 25WECh. 8.2 - Prob. 26WECh. 8.2 - Prob. 27WECh. 8.2 - Prob. 28WECh. 8.2 - Prob. 29WECh. 8.2 - Prob. 30WECh. 8.2 - Prob. 31WECh. 8.2 - Prob. 32WECh. 8.2 - Prob. 33WECh. 8.2 - Prob. 34WECh. 8.2 - Prob. 35WECh. 8.2 - Prob. 36WECh. 8.2 - Prob. 37WECh. 8.2 - Prob. 38WECh. 8.2 - Prob. 39WECh. 8.2 - Prob. 1MRECh. 8.2 - Prob. 2MRECh. 8.2 - Prob. 3MRECh. 8.2 - Prob. 4MRECh. 8.2 - Prob. 5MRECh. 8.2 - Prob. 6MRECh. 8.2 - Prob. 7MRECh. 8.3 - Prob. 1CECh. 8.3 - Prob. 2CECh. 8.3 - Prob. 3CECh. 8.3 - Prob. 4CECh. 8.3 - Prob. 5CECh. 8.3 - Prob. 6CECh. 8.3 - Prob. 7CECh. 8.3 - Prob. 8CECh. 8.3 - Prob. 9CECh. 8.3 - Prob. 10CECh. 8.3 - Prob. 1WECh. 8.3 - Prob. 2WECh. 8.3 - Prob. 3WECh. 8.3 - Prob. 4WECh. 8.3 - Prob. 5WECh. 8.3 - Prob. 6WECh. 8.3 - Prob. 7WECh. 8.3 - Prob. 8WECh. 8.3 - Prob. 9WECh. 8.3 - Prob. 10WECh. 8.3 - Prob. 11WECh. 8.3 - Prob. 12WECh. 8.3 - Prob. 13WECh. 8.3 - Prob. 14WECh. 8.3 - Prob. 15WECh. 8.3 - Prob. 16WECh. 8.3 - Prob. 17WECh. 8.3 - Prob. 18WECh. 8.3 - Prob. 19WECh. 8.3 - Prob. 20WECh. 8.3 - Prob. 21WECh. 8.3 - Prob. 22WECh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.4 - Prob. 1CECh. 8.4 - Prob. 2CECh. 8.4 - Prob. 3CECh. 8.4 - Prob. 4CECh. 8.4 - Prob. 5CECh. 8.4 - Prob. 6CECh. 8.4 - Prob. 7CECh. 8.4 - Prob. 8CECh. 8.4 - Prob. 9CECh. 8.4 - Prob. 10CECh. 8.4 - Prob. 11CECh. 8.4 - Prob. 12CECh. 8.4 - Prob. 1WECh. 8.4 - Prob. 2WECh. 8.4 - Prob. 3WECh. 8.4 - Prob. 4WECh. 8.4 - Prob. 5WECh. 8.4 - Prob. 6WECh. 8.4 - Prob. 7WECh. 8.4 - Prob. 8WECh. 8.4 - Prob. 9WECh. 8.4 - Prob. 10WECh. 8.4 - Prob. 11WECh. 8.4 - Prob. 12WECh. 8.4 - Prob. 13WECh. 8.4 - Prob. 14WECh. 8.4 - Prob. 15WECh. 8.4 - Prob. 16WECh. 8.4 - Prob. 17WECh. 8.4 - Prob. 18WECh. 8.4 - Prob. 19WECh. 8.4 - Prob. 20WECh. 8.4 - Prob. 21WECh. 8.4 - Prob. 22WECh. 8.4 - Prob. 23WECh. 8.4 - Prob. 24WECh. 8.4 - Prob. 25WECh. 8.4 - Prob. 26WECh. 8.4 - Prob. 27WECh. 8.4 - Prob. 28WECh. 8.4 - Prob. 29WECh. 8.4 - Prob. 30WECh. 8.4 - Prob. 31WECh. 8.4 - Prob. 32WECh. 8.4 - Prob. 33WECh. 8.4 - Prob. 34WECh. 8.4 - Prob. 35WECh. 8.4 - Prob. 36WECh. 8.4 - Prob. 37WECh. 8.4 - Prob. 38WECh. 8.4 - Prob. 39WECh. 8.4 - Prob. 1ST1Ch. 8.4 - Prob. 2ST1Ch. 8.4 - Prob. 3ST1Ch. 8.4 - Prob. 4ST1Ch. 8.4 - Prob. 5ST1Ch. 8.4 - Prob. 6ST1Ch. 8.4 - Prob. 7ST1Ch. 8.5 - Prob. 1CECh. 8.5 - Prob. 2CECh. 8.5 - Prob. 3CECh. 8.5 - Prob. 4CECh. 8.5 - Prob. 5CECh. 8.5 - Prob. 6CECh. 8.5 - Prob. 7CECh. 8.5 - Prob. 8CECh. 8.5 - Prob. 9CECh. 8.5 - Prob. 10CECh. 8.5 - Prob. 11CECh. 8.5 - Prob. 1WECh. 8.5 - Prob. 2WECh. 8.5 - Prob. 3WECh. 8.5 - Prob. 4WECh. 8.5 - Prob. 5WECh. 8.5 - Prob. 6WECh. 8.5 - Prob. 7WECh. 8.5 - Prob. 8WECh. 8.5 - Prob. 9WECh. 8.5 - Prob. 10WECh. 8.5 - Prob. 11WECh. 8.5 - Prob. 12WECh. 8.5 - Prob. 13WECh. 8.5 - Prob. 14WECh. 8.5 - Prob. 15WECh. 8.5 - Prob. 16WECh. 8.5 - Prob. 17WECh. 8.5 - Prob. 18WECh. 8.5 - Prob. 19WECh. 8.5 - Prob. 20WECh. 8.5 - Prob. 21WECh. 8.5 - Prob. 22WECh. 8.5 - Prob. 23WECh. 8.5 - Prob. 24WECh. 8.5 - Prob. 25WECh. 8.5 - Prob. 26WECh. 8.5 - Prob. 27WECh. 8.5 - Prob. 28WECh. 8.5 - Prob. 29WECh. 8.5 - Prob. 30WECh. 8.6 - Prob. 1CECh. 8.6 - Prob. 2CECh. 8.6 - Prob. 3CECh. 8.6 - Prob. 4CECh. 8.6 - Prob. 5CECh. 8.6 - Prob. 6CECh. 8.6 - Prob. 7CECh. 8.6 - Prob. 8CECh. 8.6 - Prob. 9CECh. 8.6 - Prob. 10CECh. 8.6 - Prob. 11CECh. 8.6 - Prob. 12CECh. 8.6 - Prob. 13CECh. 8.6 - Prob. 14CECh. 8.6 - Prob. 15CECh. 8.6 - Prob. 1WECh. 8.6 - Prob. 2WECh. 8.6 - Prob. 3WECh. 8.6 - Prob. 4WECh. 8.6 - Prob. 5WECh. 8.6 - Prob. 6WECh. 8.6 - Prob. 7WECh. 8.6 - Prob. 8WECh. 8.6 - Prob. 9WECh. 8.6 - Prob. 10WECh. 8.6 - Prob. 11WECh. 8.6 - Prob. 12WECh. 8.6 - Prob. 13WECh. 8.6 - Prob. 14WECh. 8.6 - Prob. 15WECh. 8.6 - Prob. 16WECh. 8.6 - Prob. 17WECh. 8.6 - Prob. 18WECh. 8.6 - Prob. 19WECh. 8.6 - Prob. 20WECh. 8.6 - Prob. 21WECh. 8.6 - Prob. 22WECh. 8.6 - Prob. 23WECh. 8.6 - Prob. 24WECh. 8.6 - Prob. 25WECh. 8.6 - Prob. 26WECh. 8.7 - Prob. 1CECh. 8.7 - Prob. 2CECh. 8.7 - Prob. 3CECh. 8.7 - Prob. 4CECh. 8.7 - Prob. 5CECh. 8.7 - Prob. 6CECh. 8.7 - Prob. 7CECh. 8.7 - Prob. 1WECh. 8.7 - Prob. 2WECh. 8.7 - Prob. 3WECh. 8.7 - Prob. 4WECh. 8.7 - Prob. 5WECh. 8.7 - Prob. 6WECh. 8.7 - Prob. 7WECh. 8.7 - Prob. 8WECh. 8.7 - Prob. 9WECh. 8.7 - Prob. 10WECh. 8.7 - Prob. 11WECh. 8.7 - Prob. 12WECh. 8.7 - Prob. 13WECh. 8.7 - Prob. 14WECh. 8.7 - Prob. 1ST2Ch. 8.7 - Prob. 2ST2Ch. 8.7 - Prob. 3ST2Ch. 8.7 - Prob. 4ST2Ch. 8.7 - Prob. 5ST2Ch. 8.7 - Prob. 6ST2Ch. 8.7 - Prob. 7ST2Ch. 8.7 - Prob. 8ST2Ch. 8.7 - Prob. 9ST2Ch. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Prob. 8CRCh. 8 - Prob. 9CRCh. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 14CRCh. 8 - Prob. 15CRCh. 8 - Prob. 16CRCh. 8 - Prob. 17CRCh. 8 - Prob. 18CRCh. 8 - Prob. 19CRCh. 8 - Prob. 20CRCh. 8 - Prob. 21CRCh. 8 - Prob. 22CRCh. 8 - Prob. 23CRCh. 8 - Prob. 24CRCh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - Prob. 10CTCh. 8 - Prob. 11CTCh. 8 - Prob. 12CTCh. 8 - Prob. 13CTCh. 8 - Prob. 14CTCh. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 19CTCh. 8 - Prob. 20CTCh. 8 - Prob. 21CTCh. 8 - Prob. 22CTCh. 8 - Prob. 23CTCh. 8 - Prob. 24CTCh. 8 - Prob. 25CTCh. 8 - Prob. 26CTCh. 8 - Prob. 27CTCh. 8 - Prob. 1CURCh. 8 - Prob. 2CURCh. 8 - Prob. 3CURCh. 8 - Prob. 4CURCh. 8 - Prob. 5CURCh. 8 - Prob. 6CURCh. 8 - Prob. 7CURCh. 8 - Prob. 8CURCh. 8 - Prob. 9CURCh. 8 - Prob. 10CURCh. 8 - Prob. 11CURCh. 8 - Prob. 12CURCh. 8 - Prob. 13CURCh. 8 - Prob. 14CURCh. 8 - Prob. 15CURCh. 8 - Prob. 16CURCh. 8 - Prob. 17CUR
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