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The graphic shows a spidercam used for aerial coverage of sports events - Leaving Cert DCG - Question A-4 - 2018
Question A-4
The graphic shows a spidercam used for aerial coverage of sports events. It is supported by four cables. The drawing shows the projections of the cables. (a) Find th... show full transcript
Worked Solution & Example Answer:The graphic shows a spidercam used for aerial coverage of sports events - Leaving Cert DCG - Question A-4 - 2018
Step 1
Find the dihedral angle between the planes OAB and OAD.
Answer
To determine the dihedral angle between the planes OAB and OAD, we begin by identifying the key components. The planes are defined by the lines OA, OB, and OD.
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Identify the projection lines: The projection of the lines on the X1Y1 plane must be examined. Ensure that the line OY is parallel to OA.
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Draw the auxiliary planes: Create a second projection on the X2Y2 plane, ensuring that both OAB and OAD are represented correctly.
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Construct edge views: Construct views that represent the edges OAB and OAD accurately when viewed from a perpendicular perspective to the line OA.
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Calculate the dihedral angle: Use the relevant geometric principles to calculate the dihedral angle, incorporating the necessary formulas depending on the angle properties of the projections.
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Indicate the required dihedral angle: Finally, state the calculated angle clearly.
Step 2
Determine the angle between lines OA and OB.
Answer
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Required construction to determine True Shape of triangle BOA: Utilize the triangle properties to find the length and angles in triangle BOA. This will involve practical drawing techniques to visualize the triangle effectively.
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Identification of required true angle between cables OA and OB: Once the dimensions are established from the triangle BOA, use trigonometric relationships or vector calculations as appropriate to determine the angle between the cables OA and OB. This angle is essential for understanding the spatial relationship between the two cables.