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The image on the right shows the entrance structure to the Pillo Hotel in Co - Leaving Cert DCG - Question B-3 - 2019
Question B-3
The image on the right shows the entrance structure to the Pillo Hotel in Co. Meath. It comprises a series of planar glass surfaces. Fig. B-3 shows the plan and ele... show full transcript
Worked Solution & Example Answer:The image on the right shows the entrance structure to the Pillo Hotel in Co - Leaving Cert DCG - Question B-3 - 2019
Step 1
Draw the plan and elevation of the intersecting planes A and B.
Answer
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Establish the coordinates of planes A and B in the plan by identifying key points from the figure.
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Create a scaled plan view on the given grid, accurately representing planes A and B based on the coordinates.
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For the elevation, project the plan view upward to reflect the heights of planes A and B, ensuring the parallelism of edges and intersection lines.
Step 2
Determine the dihedral angle between the planes A and B.
Answer
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Identify the line of intersection between planes A and B, using the coordinates from the previously drawn elevations.
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Project perpendicular lines from a point on plane A to the line of intersection on the new X,Y plan.
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Measure the angle formed between the normal to plane A and the line of intersection using trigonometric methods. Calculate the dihedral angle using:
ext{Dihedral Angle} = an^{-1} rac{h_{A}}{d_{A}}
where is the height and is the distance.
Step 3
Project an auxiliary elevation of plane A on the X,Y line. Hence determine, and indicate in degrees, the inclination of plane A to the horizontal plane.
Answer
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Project the auxiliary elevation of plane A down to the XY line to define its orientation on this horizontal plane.
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Determine the angle of inclination by constructing a right triangle where the vertical leg represents the height of plane A and the horizontal leg represents the corresponding distance on the XY plane.
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Use trigonometry to find the angle:
ext{Inclination} = an^{-1} rac{ ext{height of A}}{ ext{run}}. \n 4. Indicate this angle in degrees.
Step 4
Determine the points of intersection of the line PQ with the planes A and B.
Answer
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Draw the projections of line PQ onto the plan and elevation of the intersecting planes A and B.
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Analyze the path of line PQ as it intersects the planes; adjust the line to conform with proper scaling on the grid.
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Mark the points of intersection by utilizing geometric constructions to establish penetration points in both plan and elevation drawings.
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Label the intersection points clearly to indicate where line PQ meets planes A and B.