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The graphic below shows the Derry Peace Bridge, which contains two inclined pylons supporting the cable structure - Leaving Cert DCG - Question A-4 - 2015

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Question A-4

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The graphic below shows the Derry Peace Bridge, which contains two inclined pylons supporting the cable structure. The two pylons are represented by the skew lines ... show full transcript

Worked Solution & Example Answer:The graphic below shows the Derry Peace Bridge, which contains two inclined pylons supporting the cable structure - Leaving Cert DCG - Question A-4 - 2015

Step 1

Creating a plane containing CD (or AB) and parallel to AB (or CD)

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To start the projection process, create a plane that contains one of the skew lines (for instance, line CD) and is parallel to either AB or CD. This will help visualize the intersection of the lines and establish a foundational reference for the projection.

Step 2

Elevation and plan of horizontal line between parallel line

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Next, draw the elevation and plan of the horizontal line that connects projections of points B and D. It's essential to represent this line maintaining the angles that reflect the true physical relationship in the overall structure.

Step 3

XY1 perpendicular to plan of horizontal line

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Now, construct line XY1 that is perpendicular to the plan of the horizontal line, ensuring that the true lengths and angles are preserved. This step is crucial to identifying the exact locations of points A and Y on the elevation.

Step 4

Projections of lines in 1st auxiliary elevation

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After establishing XY1, proceed to project points A and B in the first auxiliary elevation parallel to line XY. This allows for a clearer understanding of how these points relate spatially to one another.

Step 5

XY2 perpendicular to XY1

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From there, draw line XY2 perpendicular to XY1. This intersection creates a new perspective of the overall structure and aids in finding the shortest distance between the two skew lines.

Step 6

Identification of shortest horizontal distance in 2nd auxiliary

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Identify the shortest horizontal distance in the second auxiliary view, ensuring that your markers indicate the relationship between the horizontal line and the skew lines.

Step 7

Draw required projections (projecting or measuring to plan and elevation)

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Finally, draw the necessary projections to represent the lines accurately in both plan and elevation views, making sure to label and highlight all critical measurements.

Step 8

Extend line to meet V.P.

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Extend the line to meet the vertical plane (V.P.), ensuring that its endpoint is clearly marked in relation to the other lines in the image.

Step 9

Indicate required angle

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Answer

Indicate the required angle between the horizontal line and the vertical plane in degrees, using a protractor or angle measuring tool for accuracy.

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