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The image shows a multi-storey building in Chicago - Leaving Cert DCG - Question A-1 - 2019
Question A-1
The image shows a multi-storey building in Chicago. The front of the structure is comprised of a series of glass panels. The drawing shows the projections of three s... show full transcript
Worked Solution & Example Answer:The image shows a multi-storey building in Chicago - Leaving Cert DCG - Question A-1 - 2019
Step 1
Determine the dihedral angle between the surfaces abc and bcd
Answer
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Identify the Line of Intersection:
- The line 'be' represents the intersection between the two planes abc and bcd.
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Draw Projections:
- Project point P vertically to establish the X,Y plane, ensuring that X1 and Y1 are parallel to the line of intersection.
- This helps in visualizing the angles involved.
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Auxiliary Views:
- Draw the auxiliary views for surfaces 'abe' and 'bed' to depict the necessary relationships.
- In the first auxiliary view, show the relationship between edges and surfaces for better understanding.
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Identify Key Projections:
- Establish perpendicular lines to the line of intersection from point P for both surfaces.
- Note projections to both X1, Y1 and X2, Y2 accordingly to illustrate the required angles.
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Determine the Required Dihedral Angle:
- Analyze the formed angles at the intersection line, calculating using the cosine or sine rules based on the projections.
- The dihedral angle is then represented based on the calculated observations.
Step 2
Draw the elevation and plan of a horizontal line on surface cdp which shall pass through point P
Answer
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Draw the Required Horizontal Line in Elevation:
- From point P, draw a horizontal line along surface cdp to visualize its position relative to the elevation view.
- Ensure the line remains on the plane of the surface and marks the point of intersection with other reference lines.
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Draw the Required Horizontal Line in Plan:
- Project point P onto the plan view, extending the horizontal line appropriately within the plane 'cdp'.
- Align the line parallel to the horizontal reference to maintain accuracy.
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Determine and Indicate Angle:
- Measure the inclination of this horizontal line to the vertical plane.
- Use trigonometric relationships to find the angle, expressing this in degrees on your drawing.
- Clearly indicate the angle alongside the horizontal line in both elevation and plan views for clarity.