(a) Answer Longer diagonal = 68.15 inches Explanation Given information: Geometry: The lengths of two sides of a parallelogram are 48 inches and 30 inches. One angle measures 120 ∘ Calculation: Use law of cosines to solve for the longer diagonal. c = 30 2 + 48 2 − 2 ( 30 ) ( 48 ) cos ( 120 ∘ ) Simplify and solve for the longer diagonal. c = 68.15 Thus, Longer diagonal = 68.15 inches (b) To determine To find: The area of the parallelogram. Answer Area = 1274.83 u 2 Explanation Given information: Geometry: The lengths of two sides of a parallelogram are 48 inches and 30 inches. One angle measures 120 ∘ Calculation: Find s to use Heron’s formula s = 30 + 48 + 68.15 2 Solve for s s = 73.08 Use Heron’s formula to find the area of the triangle. A = 73.08 ( 73.08 − 30 ) ( 73.08 − 48 ) ( 73.08 − 68.15 ) Simplify and solve for the area of the triangle A = 623.91 u 2 Multiply by two to solve for the area of the parallelogram. A = 623.91 u 2 × 2 = 1247.83 u 2 Thus, Area = 1247.83 u 2

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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Question

Chapter 5.8, Problem 25E

(a)

To determine

To find: The length of the longer diagonal.

(a)

Expert Solution

Answer to Problem 25E

Longer diagonal = 68.15 inches

Explanation of Solution

Given information: Geometry: The lengths of two sides of a parallelogram are 48 inches and 30 inches. One angle measures 120∘

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.8, Problem 25E , additional homework tip 1

Calculation:

Use law of cosines to solve for the longer diagonal.

c=302+482−2(30)(48)cos(120∘)

Simplify and solve for the longer diagonal.

c=68.15

Thus,

Longer diagonal = 68.15 inches

(b)

To determine

To find: The area of the parallelogram.

(b)

Expert Solution

Answer to Problem 25E

Area=1274.83u2

Explanation of Solution

Given information: Geometry: The lengths of two sides of a parallelogram are 48 inches and 30 inches. One angle measures 120∘

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.8, Problem 25E , additional homework tip 2

Calculation:

Find s to use Heron’s formula

s=30+48+68.152

Solve for s

s=73.08

Use Heron’s formula to find the area of the triangle.

A=73.08(73.08−30)(73.08−48)(73.08−68.15)

Simplify and solve for the area of the triangle

A=623.91u2

Multiply by two to solve for the area of the parallelogram.

A=623.91u2×2=1247.83u2

Thus,

Area=1247.83u2

Chapter 5.8, Problem 24E

Chapter 5.8, Problem 26E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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