### Geometry Application in Architectural SupportAn educational segment discussing applied geometry in architecture.**Problem:**A new piece of support material needs to be installed in the triangular region on the house shown below, where $ CD = 60 $ inches, $ \angle ECD = 32^\circ $, and $ EF $ is the perpendicular bisector of $ CD $.**Diagram Description:**The diagram depicts a triangular region on the side of a house. In the triangle:- $ CD $ is the base of the triangle, with a length of 60 inches.- $ \angle ECD $ is given as $ 32^\circ $.- $ EF $ is marked as the perpendicular bisector of $ CD $, indicating it is perpendicular to $ CD $ and intersects $ CD $ at its midpoint $ E $.#### Question:To the nearest inch, what is the amount of material needed to install on the segment labeled $ FD $?**Answer Options:**- A) 57 inches- B) 36 inches- C) 25 inches- D) 71 inches(Note: The correct answer is to be calculated based on geometric principles involving triangle properties and bisectors.)**Solution Procedure:**1. Identify the given values: - $ CD = 60 $ inches - $ \angle ECD = 32^\circ $ - $ E $ is the midpoint of $ CD $, therefore $ CE = ED = 30 $ inches since $ EF $ is the perpendicular bisector.2. Apply trigonometric ratios (specifically, the sine and cosine functions) to calculate the length of the segment $ FD $.By using these methods, the precise measurement for segment $ FD $ can be calculated, ensuring the correct amount of material is selected for installation.**Diagram:**![Roof Diagram](image_url) This diagram adds a practical context to understanding basic geometric principles and their real-world application in architectural support structures.**End of Content**.

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Description: ### Geometry Application in Architectural SupportAn educational segment discussing applied geometry in architecture.**Problem:**A new piece of support material needs to be installed in the triangular region on the house shown below, where \( CD = 60

Given : CD = 60 inches <FCE = 32 EF is the perpendicular bisector of CD. To find FD

Math

Geometry

An new piece of support material needs to be instalied in the triangular region on the house shown below, where CD = 60 inches m2J CI = 32, and Fis the perpendicular bisector of ) Yo the neestach at she onoini ofinaleila 35 kmchrs 25 inches TL piches

An new piece of support material needs to be instalied in the triangular region on the house shown below, where CD = 60 inches m2J CI = 32, and Fis the perpendicular bisector of ) Yo the neestach at she onoini ofinaleila 35 kmchrs 25 inches TL piches

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Geometry Application in Architectural Support

An educational segment discussing applied geometry in architecture.

**Problem:**
A new piece of support material needs to be installed in the triangular region on the house shown below, where $ CD = 60 $ inches, $ \angle ECD = 32^\circ $, and $ EF $ is the perpendicular bisector of $ CD $.

**Diagram Description:**
The diagram depicts a triangular region on the side of a house. In the triangle:

- $ CD $ is the base of the triangle, with a length of 60 inches.
- $ \angle ECD $ is given as $ 32^\circ $.
- $ EF $ is marked as the perpendicular bisector of $ CD $, indicating it is perpendicular to $ CD $ and intersects $ CD $ at its midpoint $ E $.

#### Question:
To the nearest inch, what is the amount of material needed to install on the segment labeled $ FD $?

**Answer Options:**

- A) 57 inches
- B) 36 inches
- C) 25 inches
- D) 71 inches

(Note: The correct answer is to be calculated based on geometric principles involving triangle properties and bisectors.)

**Solution Procedure:**
1. Identify the given values:
- $ CD = 60 $ inches
- $ \angle ECD = 32^\circ $
- $ E $ is the midpoint of $ CD $, therefore $ CE = ED = 30 $ inches since $ EF $ is the perpendicular bisector.

2. Apply trigonometric ratios (specifically, the sine and cosine functions) to calculate the length of the segment $ FD $.

By using these methods, the precise measurement for segment $ FD $ can be calculated, ensuring the correct amount of material is selected for installation.

**Diagram:**

![Roof Diagram](image_url)

This diagram adds a practical context to understanding basic geometric principles and their real-world application in architectural support structures.

**End of Content**.

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