Fig. B-3 shows an incomplete trimetric projection, using the axonometric axes method, of a similar table-tennis table. The elevation and end view are shown in their required positions. A pictorial view of the table is also shown. (a) Draw the axonometric axes X, Y and Z and the scalene triangle abc. (b) Draw the elevation and end view, orientated as shown, and complete the trimetric projection. (c) Determine the true length of the diagonal along the top surface of the table.

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Fig. B-3 shows an incomplete trimetric projection, using the axonometric axes method, of a similar table-tennis table - Leaving Cert DCG - Question B-3 - 2021

Question B-3

Fig. B-3 shows an incomplete trimetric projection, using the axonometric axes method, of a similar table-tennis table. The elevation and end view are shown in their ... show full transcript

Worked Solution & Example Answer:Fig. B-3 shows an incomplete trimetric projection, using the axonometric axes method, of a similar table-tennis table - Leaving Cert DCG - Question B-3 - 2021

Step 1

Draw the axonometric axes X, Y and Z and the scalene triangle abc.

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Answer

To draw the axonometric axes, we begin by determining the orientation of axes Y and Z, which should be set at 70 degrees and 110 degrees respectively to the horizontal plane (X-axis) as per the given orientation.

Establishing Axes:
- Starting from the origin, draw the Y-axis at 70 degrees from the horizontal.
- Extend the Z-axis at 110 degrees from the horizontal, ensuring it meets at a suitable scale relative to the Y-axis.
- Finally, draw the X-axis horizontally.
Drawing the Scalene Triangle abc:
- Mark point a at (0, 25) on the Y axis, point b at (-25, 50) on the Z-axis, and point c at (50, 0) on the X-axis, ensuring all sides are unequal, conforming to the scalene triangle definition.

Step 2

Draw the elevation and end view, orientated as shown, and complete the trimetric projection.

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Answer

Draw the Elevation:
- Represent the elevation view conservatively with respect to the X and Y axes, showing the table's height accurately.
- Ensure that the height at Y measures 25 units and at Z measures 50 units in accordance with the given dimensions.
Draw End View:
- For the end view on the XY plane, mark the length in accordance with the required dimensions (e.g., width and height).
Trimetric Projection Completion:
- Project points from the elevation to the trimetric view using the determined angles for accurate positioning.
- Ensure that the curves representing the table's surface appear in the same axonometric view.

Step 3

Determine the true length of the diagonal along the top surface of the table.

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Answer

To find the true length of the diagonal (d) across the top surface of the table, we can use the formula derived from the Pythagorean Theorem:

$d = \sqrt{l^2 + w^2}$

Here,

Let the length (l) of the top surface be 70 units,
let the width (w) be 50 units.

Thus, substituting these values:

$d = \sqrt{70^2 + 50^2} = \sqrt{4900 + 2500} = \sqrt{7400} \approx 86.02$

Therefore, the true length of the diagonal along the top surface of the table is approximately 86.02 units.

Fig. B-3 shows an incomplete trimetric projection, using the axonometric axes method, of a similar table-tennis table - Leaving Cert DCG - Question B-3 - 2021

Worked Solution & Example Answer:Fig. B-3 shows an incomplete trimetric projection, using the axonometric axes method, of a similar table-tennis table - Leaving Cert DCG - Question B-3 - 2021

Draw the axonometric axes X, Y and Z and the scalene triangle abc.

Draw the elevation and end view, orientated as shown, and complete the trimetric projection.

Determine the true length of the diagonal along the top surface of the table.

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