Photo AI
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 t... 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 find the dihedral angle between planes OAB and OAD, we first need to establish the coordinates of points A, B, O, and D.
-
Identify the projection of the planes on the coordinate system:
- Observe the projections of planes OAB and OAD on the plane X1Y1, plotting points accordingly.
-
Use the auxiliary view:
- Allowing ourselves to understand the perspective, we will now refer to the auxiliary view where the intersection lines and their relationship can be clearer.
-
Establish perpendicularity:
- Ensure that the auxiliary axis Y2 is perpendicular to cable OA. This helps in visualizing the angle created between the two planes.
-
Project onto edge views:
- Project the planes OAB and OAD specifically looking at the edge views on the plane X2Y2.
-
Calculate the dihedral angle:
- With all the data gathered, apply the formula for the dihedral angle between two planes, which can be obtained from the normals of these planes.
Step 2
Determine the angle between lines OA and OB.
Answer
-
Required construction to determine the true shape of triangle BOA:
- Construct a triangle using vertices B, O, and A, ensuring accurate representation of the sides and angles involved.
-
Identification of required true angle:
- Identify the angle of interest formed between cables OA and OB within the constructed triangle.