Chapter 11.1, Problem 39E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*For Exercises 35 to 38, make drawings as needed.*

In regular pentagon *ABCD*, sides
*s*, find an expression for

a) *h*, the length of the altitude of
*B* to side

b) *d*, the length of diagonal
*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

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

Hence, the sine ratio for an acute angle is

**Given:**

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

Consider the isosceles triangle ABC,

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

Here, the interior angles of the pentagon is

Here, we have isosceles triangle so that,

To determine

**To find:**

b. The diagonal of the pentagon

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