   Chapter 11.4, Problem 29E 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 29 to 34, use the Law of Sines or the Law of Cosines to solve each problem. Angle measures should be found to the nearest degree and areas and distances to the nearest tenth of a unit.A triangular lot has street dimensions of 150  ft and 180  ft and an included angle of 80 ∘ for these two sides.a) Find the length of the remaining side of the lot.b) Find the area of the lot in square feet.

To determine

a.

To find:

The length of the remaining side of the triangular lot.

Explanation

Formula:

The Law of Cosines

a2=b2+c22bccosα

b2=a2+c22accosβ

c2=a2+b22abcosγ

Where α, β, and γ is the acute angle of the triangle, and a, b, and c is the sides of the triangle.

Calculation:

Given,

A triangular lot has street dimensions of 150 ft 180 ft with angle 80°.

From the figure,

a=BC=150ft, b=AC=180ftand c=γ=80°

Let c=AB=x

Find x:

By the law of cosines,

To determine

b.

To find:

The area of the triangular lot in square ft.

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