Answer The length of each diagonal of rhombusis 25.4 and 54.4 . Explanation Given information: The side of rhombus is 30 unit and the angle with diagonal is 25 ° . Calculation: Consider the figure. From triangle ABO, sin 25 = x 30 x = 30 sin 25 x = 12.7 The length of Diagonal AC is, 2 x = 2 ( 12.7 ) = 25.4 From triangle ABO, cos 25 = y 30 y = 30 cos 25 y = 27.2 The length of Diagonal BD is, 2 y = 2 ( 27.2 ) = 54.4 Thus, the length of each diagonal of rhombus is 25.4 and 54.4 .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Question

Chapter 6.8, Problem 49E

To determine

Tofind:The length of each diagonal of rhombus.

Expert Solution & Answer

Answer to Problem 49E

The length of each diagonal of rhombusis 25.4 and 54.4 .

Explanation of Solution

Given information:The side of rhombus is 30 unit and the angle with diagonal is 25° .

Calculation:

Consider the figure.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 6.8, Problem 49E

From triangle ABO,

sin25=x30x=30sin25x=12.7

The length of Diagonal AC is,

2x=2(12.7)=25.4

From triangle ABO,

cos25=y30y=30cos25y=27.2

The length of Diagonal BD is,

2y=2(27.2)=54.4

Thus, the length of each diagonal of rhombus is 25.4 and 54.4 .

Chapter 6.8, Problem 48E

Chapter 6.8, Problem 50E

Chapter 6 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 6.1 - Prob. 1CFU Ch. 6.1 - Prob. 2CFU Ch. 6.1 - Prob. 3CFU Ch. 6.1 - Prob. 4CFU Ch. 6.1 - Prob. 5CFU Ch. 6.1 - Prob. 6CFU Ch. 6.1 - Prob. 7CFU Ch. 6.1 - Prob. 8CFU Ch. 6.1 - Prob. 9CFU Ch. 6.1 - Prob. 10CFU

Ch. 6.1 - Prob. 11CFU Ch. 6.1 - Prob. 12CFU Ch. 6.1 - Prob. 13CFU Ch. 6.1 - Prob. 14CFU Ch. 6.1 - Prob. 15CFU Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - 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