Unit 1ProjectionsEASY
True Length and Inclinations of a Line
A line AB, 80mm long, has its end A 20mm above HP and 25mm in front of VP. End B is 50mm above HP and 60mm in front of VP. Determine the true length and its inclinations with HP and VP.
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Solution Diagram
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Step-by-Step Construction
- 1
Plot the projections of points A and B using given coordinates
- 2
Draw the front view (FV) and top view (TV) of the line
- 3
Apply the theorem: True Length = √[(FV length)² + (difference in distances from VP)²]
- 4
Calculate angle with HP using tan θ = (height difference) / (TV length)
- 5
Calculate angle with VP using tan φ = (depth difference) / (FV length)
- 6
Verify using graphical method with auxiliary projection
Pro Tips
- •Always verify your measurements with a scale before finalizing the drawing
- •Use construction lines lightly and darken the final solution
- •Label all important points and reference lines clearly