True length of a segment
The right-triangle method – a view never misreports a length by accident.
Orbit the space
Theory
A projection nearly always foreshortens a segment. You can read the true size off a view only when the segment is parallel to that image plane – a horizontal segment appears true in the top view, a frontal one in the front view.
In general position we use the right-triangle method. One leg is the plan length |A₁B₁|, the other is the height difference Δz = |z_B − z_A|. The true length is the hypotenuse.
It is not a trick but the Pythagorean theorem in space: |AB| = √(|A₁B₁|² + Δz²). Spatially it is a right triangle with one horizontal and one vertical leg – which is why they must be perpendicular.
Step-by-step construction
Practice
Build the construction yourself
What is the next step?
1 / 4Choose the step that comes next. The drawing only advances on a correct choice.
Check your understanding
When does a segment appear in true size in the top view?
What are the legs of the right triangle used to find the true length of AB?
The plan of a segment measures 4 and the height difference is 3. What is the true length?
Exercises for this lesson
Practise in the Sandbox or the 3D Lab – your solution is checked automatically.
Distance from a plane
Level 33D LabFoot of the normal
Level 33D LabTrue length of a segment
Level 4SandboxMetricRotating the projecting plane
Level 4SandboxMetricclassicalPerpendicular to a plane
Level 4SandboxMetricDistance of a point from a plane
Level 4SandboxMetricDistance of a point from a line
Level 4SandboxMetricTrue shape of a triangle
Level 4SandboxMetricInclination of a line to π₁
Level 4SandboxMetricInclination of a plane to π₁
Level 4SandboxMetricAngle of a line and a plane
Level 4SandboxMetricAltitude of a triangle
Level 4SandboxMetricA plane perpendicular to a plane
Level 4SandboxMetricDistance of skew lines
Level 43D LabAngle of two planes
Level 43D LabAngle of a line and a plane
Level 43D LabDistance of parallel planes
Level 5SandboxMetricCommon perpendicular of skew lines
Level 5SandboxMetricDistance from a line
Level 53D Lab
Downloadable material
A PDF for this lesson is in preparation.
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