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The image on the right shows a restaurant which consists of a series of intersecting triangular glass surfaces - Leaving Cert DCG - Question B-1 - 2016
Question B-1
The image on the right shows a restaurant which consists of a series of intersecting triangular glass surfaces. Fig. B-1 shows the plan and elevation of four such i... show full transcript
Worked Solution & Example Answer:The image on the right shows a restaurant which consists of a series of intersecting triangular glass surfaces - Leaving Cert DCG - Question B-1 - 2016
Step 1
Draw the given plan of the four triangular planes and complete the elevation of the intersecting planes ABC, ABD and DEB.
Answer
To begin, sketch the plan based on the coordinates provided for points A, B, C, D, E, and F as follows:
- Connect points A, B, C, D to form the triangles ABC and ABD in the plan view.
- Make sure to represent accurate measurements based on given coordinates, ensuring that the intersection lines are clearly marked.
- Next, utilize the elevation details to draw how these planes would look from the side, particularly focusing on the heights dictated by the vertical coordinates associated with each point.
Step 2
Determine the dihedral angle between the planes ABC and ABD.
Answer
The dihedral angle between planes ABC and ABD can be calculated using the angle between their normal vectors. Begin by identifying the normal vectors of both planes, which can be derived from the coordinates of points A, B, C, and D. One effective method is to use the following formula for the dihedral angle, :
heta = an^{-1} rac{|n_1 imes n_2|}{n_1 ullet n_2}
where and are the normal vectors of the planes.
Step 3
Draw the elevation and plan of a horizontal line on the surface DEB and then determine the true inclination of surface DEB to the horizontal plane.
Answer
To depict the elevation of line DEB, start with the given coordinates ensuring that it intersects correctly with the horizontal plane. The plan should illustrate this line, showing it relative to the intersecting planes. To find the true inclination of surface DEB, measure the angle between the horizontal plane and the normal to surface DEB using the formula:
ext{Inclination} = an^{-1}( rac{h}{d})
where is the height above the horizontal, and is the distance in the horizontal plane.
Step 4
The dihedral angle between the planes DEB and DEF is 170°. Complete the projections of the surface DEF.
Answer
For this part, start by drawing the plane DEF based on the identified dihedral angle of 170°. It should be positioned such that it correctly intersects with the existing planes from the previous steps. Ensure to project points D, E, and F into both plan and elevation, accounting for the angles and distances calculated earlier. Complete the drawing by connecting all projections accurately to visualize the interrelationships between the planes.