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The image on the right shows a car showroom in Qatar - Leaving Cert DCG - Question B-2 - 2021
Question B-2
The image on the right shows a car showroom in Qatar. The building includes a series of intersecting planar triangular surfaces. Fig. B-2 shows the plan and elevatio... show full transcript
Worked Solution & Example Answer:The image on the right shows a car showroom in Qatar - Leaving Cert DCG - Question B-2 - 2021
Step 1
Draw the given elevation and plan of the intersecting planes ABC, ABD, and BDE.
Answer
- Begin by plotting points A, B, C, D, and E based on the provided coordinates.
- Create the elevation and plan views for plane ABC:
- Connect points A to B and C to form triangle ABC in both views. Ensure the dimensions are accurate based on the coordinates provided.
- Repeat this for plane ABD:
- Connect points A, B, and D.
- Finally, draw plane BDE using points B, D, and E.
- Ensure all planes are drawn to scale (1:1) as indicated.
Step 2
Determine the dihedral angle between the planes ABC and ABD.
Answer
- Identify the line of intersection between planes ABC and ABD, which runs along edge AB.
- Construct the projections of both planes and use the angles formed between the lines created by the two planes.
- Use the formula for dihedral angles: heta = an^{-1} rac{h_1 - h_2}{d} where and are the heights at points A and B respectively, and is the horizontal distance between them.
Step 3
A line is drawn from the point E. This line is parallel to the line AC and intersects the horizontal plane at a point P.
Answer
- From point E, draw a line parallel to line AC. Ensure this line intersects the horizontal plane.
- Mark the intersection point as P.
- Project point P vertically down to determine its true position in the elevation view.
Step 4
Draw the projections of line EP and determine its inclination to HP.
Answer
- To draw the projections of line EP:
- Start by plotting point E and the intersection point P on the plan.
- Draw vertical lines from both points to form their projections in the elevation view.
- To determine the inclination of EP to the horizontal plane:
- Use the perpendicular distances to infer the angle of inclination.
- Apply trigonometric relationships, such as: an( heta) = rac{h}{d} where is the vertical length of EP and is the horizontal distance.
Step 5
Complete the projections of the triangle ACF.
Answer
- Start by drawing the true length of edges AF and CF from point A in the plan view.
- For edge AF = 70mm, draw an arc from point A.
- For edge CF = 80mm, determine its line in relation to the established references in the projection.
- Label each vertex appropriately and ensure that all angles are maintained according to their elevations in both views.
- Finalize the triangle ACF with complete projection lines indicating their respective elevations.