a ) Answer The measure of angle ABD to the nearest tenth of a degree = 44.5 ° Explanation Given: In the given figure on line AC two adjacent angles ∠ A B D = ( 812 x ) ° , ∠ D B C = (2469 x ) ° are marked Concept Used : Two adjacent angles standing on a straight line form a linear pair which means they add up to 180 ° Calculation : As per the given figure ∠ A B D , ∠ D B C form a linear pair. So, ∠ ABD + ∠ D B C = 180 ° also ∠ A B D = ( 812 x ) ° , ∠ D B C = (2469 x ) ° .Which means: ∠ A B D + ∠ D B C = 180 ° ⇒ ( 812 x ) ° + ( 2469 x ) ° = 180 ° ⇒ (3281 x ) ° = 180 ° ⇒ x = ( 180 ° 3281 ° ) ⇒ x = 0 .05486 (Taking value up to 5 decimal places) So, ∠ A B D = (812 x ) ° ⇒ ∠ ABD = (812 × 0 .05486) ° = 44 .54632 ° Converting this value to the nearest tenth place we will get 44 .54632 ° = 44 .5 ° Conclusion: The measure of angle ABD to the nearest tenth of a degree = 44.5 ° b) To determine To Find: The measure of given angle to its nearest minute Answer The measure of given angle to its nearest minute = 44 ° 33 ' Explanation Given: In the given figure on line AC two adjacent angles ∠ A B D = ( 812 x ) ° , ∠ D B C = (2469 x ) ° are marked Concept Used : Two adjacent angles standing on a straight line form a linear pair which means they add up to 180 ° Calculation : As per the given figure ∠ A B D , ∠ D B C form a linear pair. So, ∠ ABD + ∠ D B C = 180 ° also ∠ A B D = ( 812 x ) ° , ∠ D B C = (2469 x ) ° .Which means: ∠ A B D + ∠ D B C = 180 ° ⇒ ( 812 x ) ° + ( 2469 x ) ° = 180 ° ⇒ (3281 x ) ° = 180 ° ⇒ x = ( 180 ° 3281 ° ) ⇒ x = 0 .05486 (Taking value up to 5 decimal places) So, ∠ A B D = (812 x ) ° ⇒ ∠ ABD = (812 × 0 .05486) ° = 44 .54632 ° Converting 44 .54632 ° into minutes by multiplying decimal part by 60 0 .54632 ° × 60 = 32 .7792 minutes Writing it to the nearest minute we will get : 44 ° 33 ' Conclusion: The measure of given angle to its nearest minute = 44 ° 33 '

91st Edition

ISBN: 9780866099653

Author: Richard Rhoad, George Milauskas, Robert Whipple

Publisher: McDougal Littell

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 1, Problem 31RP

a )

To determine

To Find : The measure of angle ABD to the nearest tenth of a degree

a )

Expert Solution

Answer to Problem 31RP

The measure of angle ABD to the nearest tenth of a degree = $44.5°$

Explanation of Solution

Given: In the given figure on line AC two adjacent angles $∠ABD=(812x)° , ∠DBC = (2469x)°$ are marked

Concept Used: Two adjacent angles standing on a straight line form a linear pair which means they add up to $180°$

Calculation: As per the given figure $∠ABD$ , $∠DBC$ form a linear pair. So,

$∠ABD + ∠DBC = 180°$ also $∠ABD=(812x)° , ∠DBC = (2469x)°$ .Which means:

$∠ABD + ∠DBC = 180°⇒(812x)°+ ( 2469x)° = 180°⇒ (3281x)° = 180°⇒x = (180°3281°)⇒x = 0.05486$

(Taking value up to $5$ decimal places)

So, $∠ABD = (812x)°⇒ ∠ABD = (812 × 0.05486)° = 44.54632°$

Converting this value to the nearest tenth place we will get $44.54632° = 44.5°$

Conclusion:

The measure of angle ABD to the nearest tenth of a degree = $44.5°$

To determine

To Find: The measure of given angle to its nearest minute

Expert Solution

Answer to Problem 31RP

The measure of given angle to its nearest minute $= 44° 33 '$

Explanation of Solution

Given: In the given figure on line AC two adjacent angles $∠ABD=(812x)° , ∠DBC = (2469x)°$ are marked

Concept Used: Two adjacent angles standing on a straight line form a linear pair which means they add up to $180°$

Calculation: As per the given figure $∠ABD$ , $∠DBC$ form a linear pair. So,

$∠ABD + ∠DBC = 180°$ also $∠ABD=(812x)° , ∠DBC = (2469x)°$ .Which means:

$∠ABD + ∠DBC = 180°⇒(812x)°+ ( 2469x)° = 180°⇒ (3281x)° = 180°⇒x = (180°3281°)⇒x = 0.05486$

(Taking value up to $5$ decimal places)

So, $∠ABD = (812x)°⇒ ∠ABD = (812 × 0.05486)° = 44.54632°$

Converting $44.54632°$ into minutes by multiplying decimal part by $60$

$0.54632 ° × 60 = 32.7792 minutes$

Writing it to the nearest minute we will get : $44° 33 '$

Conclusion:

The measure of given angle to its nearest minute $= 44° 33 '$

Chapter 1, Problem 30RP

Chapter 1, Problem 32RP

Chapter 1 Solutions

Geometry For Enjoyment And Challenge

Ch. 1.1 - Prob. 1PSA Ch. 1.1 - Prob. 2PSA Ch. 1.1 - Prob. 3PSA Ch. 1.1 - Prob. 4PSA Ch. 1.1 - Prob. 5PSA Ch. 1.1 - Prob. 6PSA Ch. 1.1 - Prob. 7PSA Ch. 1.1 - Prob. 8PSA Ch. 1.1 - Prob. 9PSA Ch. 1.1 - Prob. 10PSA

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