   Chapter 11.4, Problem 1E 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) a = 5 ,   b = 6 ,  and  γ = 78 ∘ b) a = 5 ,   b = 7 ,   α = 36 ∘  and  β = 88 ∘ Exercises 1-8

To determine

a)

To find:

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

If a=5, b=6, and γ=78

Explanation

1) Formula:

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=12absinγ

2) Calculation:

Given,

In triangle ABC,

a=5b=6 andγ=78

The area of the triangle ABC A=12absinγ

To determine

b)

To find:

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

If a=5, b=7, α=36 and β=88

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