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The image on the right shows a playground unit incorporating two planar surfaces which intersect as shown to represent the bow of a boat - Leaving Cert DCG - Question B-2 - 2017
Question B-2
The image on the right shows a playground unit incorporating two planar surfaces which intersect as shown to represent the bow of a boat. The unit includes a triangu... show full transcript
Worked Solution & Example Answer:The image on the right shows a playground unit incorporating two planar surfaces which intersect as shown to represent the bow of a boat - Leaving Cert DCG - Question B-2 - 2017
Step 1
Draw the plan and elevation of the two intersecting planes ABCD and ABFE.
Answer
Using the given coordinates, plot points A, B, C, D, E, and F on the plan and elevation views. Connect these points according to their respective coordinates to create the intersection of the planes. Ensure the angles and lines make sense visually to represent the three-dimensional nature of the unit.
Step 2
Determine the dihedral angle between the planes.
Answer
To find the dihedral angle between planes ABCD and ABFE, identify the line of intersection AB. Use the normal vectors of each plane at this line to calculate the angle using the formula:
ext{cos}( heta) = rac{N_1 ullet N_2}{|N_1| |N_2|}
where and are the normal vectors for planes ABCD and ABFE, respectively. This will provide the angle between the two planes.
Step 3
Determine the true shape of the surface ABCD.
Answer
To find the true shape of ABCD, first project the points A, B, C, and D onto the reference line. Construct the true shape by measuring distances and angles accurately. Incorporate a Ø20mm circle for the porthole at the specified location of 30mm from line AB and 50mm from point D. Ensure proper scales are maintained for accuracy.
Step 4
Draw the elevation and plan of the seat.
Answer
Join the midpoints of lines AB, AD, and EF to form the outline of the seat in the elevation and plan views. Accurately represent the seat dimensions and angles according to the intersections. Then, indicate the horizontal and vertical traces of the oblique plane of the seat, ensuring clarity in the drawing.