   Chapter 11.1, Problem 39E 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

For Exercises 35 to 38, make drawings as needed.In regular pentagon ABCD, sides A B - and B C - , along with diagonal A C - , form isosceles △ A B C . Let A B = B C = s . In terms of s, find an expression fora) h, the length of the altitude of △ A B C from vertex B to side A C - .b) d, the length of diagonal A C - of regular pentagon ABCDE.

To determine

To find:

a. The length of altitude.

Explanation

In a right angle triangle,

1) The side PQ, which is opposite to the right angle PRQ is called the hypotenuse.

(The hypotenuse is the longest side of the right triangle.)

2) The side RQ is called the adjacent side of angle θ.

3) The side PR is called the opposite side of angle θ.

Hence, the sine ratio for an acute angle is oppositehypotenuse

Given:

In a regular pentagon ABCDE, AC the diagonal of the pentagon.

Consider the isosceles triangle ABC,

AB=BC=s (opposite side)

Let h, be the altitude of the triangle(hypotenuse) from vertex B to Side AC.

Here, the interior angles of the pentagon is 108° and the exterior angles of the pentagon is 72°

Here, we have isosceles triangle so that, θ=36°

To determine

To find:

b. The diagonal of the pentagon

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