   Chapter 11.4, Problem 2E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 1 and 2, use the given information to find an expression for the area of Δ A B C . Give the answer in a form such as A = 1 2 ( 3 ) ( 4 )  sin 32 ∘ . See the figure for Exercises 1 to 8.a) b = 7.3 ,   c = 8.6 ,  and  α = 38 ∘ b) a = 5.3 ,   c = 8.4 ,   α = 36 ∘  and  γ = 87 ∘ Exercises 1-8

To determine

a)

To find:

The area of the ABC in the form of A=12(a)(b) sin α

If a=7.3, b=8.6, and α=38

Explanation

1) Approach:

The area of an acute triangle equals one-half the product of the lengths of two sides and the sine of the included angle.

The area of the triangle ABC is given by,

A=12absinα

2) Calculation:

Given,

In triangle ABC,

a=7.3b=8.6 andα=38

The area of the triangle ABC A=12absinα

A=12(7

To determine

To find:

The area of the ABC in the form of A=12(a)(b) sin γ

If a=5.3, b=8.4, α=36 and γ=87

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