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2012 marks the centenary of the sinking of the Titanic, the world's most famous ocean liner, which was built in Belfast - Leaving Cert DCG - Question B-3 - 2012
Question B-3
2012 marks the centenary of the sinking of the Titanic, the world's most famous ocean liner, which was built in Belfast. The image on the right shows the new Titani... show full transcript
Worked Solution & Example Answer:2012 marks the centenary of the sinking of the Titanic, the world's most famous ocean liner, which was built in Belfast - Leaving Cert DCG - Question B-3 - 2012
Step 1
Draw the given plan of the two intersecting planes and locate points A, B, D & F in elevation.
Answer
To begin the drawing of the two intersecting planes, we will use the provided coordinates for each point:
- A (165, 0, 70)
- B (0, 0, 25)
- D (0, 170, 0)
- F (155, 0, 25)
Using these coordinates, sketch the plan view showing lines joining the points according to the grid, then draw the elevation. Points A, B, D, and F must be clearly marked according to their elevations.
Step 2
Determine the height, h, for points C and E and complete the elevation.
Answer
To determine the height 'h' for points C and E, we first identify their base height from the horizontal plane:
For point C, based on the coordinates given: C (0, 70, h) For point E, we derive it similarly based on its relation to points on the vertical plane.
Once heights are calculated, we complete the elevation ensuring the points align correctly with the plan view.
Step 3
Determine the dihedral angle between the two planes.
Answer
To determine the dihedral angle, we begin by establishing the line of intersection between planes ABCD and ABFE. Using geometrical methods, we can calculate:
- A new line XY parallel to the line of intersection.
- Projections of point A, B, and their intersection on XY, and establish the angle between the two planes by calculating the angle formed at intersection.
The formula for the dihedral angle can be inferred as follows: ext{Dihedral Angle} = an^{-1} rac{h_1 - h_2}{d} where h1 and h2 are the heights and d is the distance between two points on the intersection.
Step 4
Determine and indicate the horizontal and vertical traces of the oblique plane that contains the surface ABFE.
Answer
To find the horizontal trace (H.T.) of plane ABFE, identify where it intersects the horizontal plane. Draw this as a line that complies with the coordinates of points A, B, and F.
The vertical trace (V.T.) is determined by projecting the intersection line onto the vertical plane. Construct the line and identify it visually in relation to heights previously calculated. Ensure all traces are clearly indicated in the drawing.