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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): True length & angles of lines

How often True length & angles of lines comes up on the Design & Communication Graphics papers, every year it was asked, and questions to try.

HL Asked on 7 of the last 9 Higher Level papers, most recently in 2024. most years

True length & angles of lines, Higher Level(8 marks)

Quick ones on True length & angles of lines.

(a)To show a line in true length in an auxiliary view projected from the plan, how is X1Y1 drawn?
  1. Perpendicular to the plan of the line
  2. Parallel to the plan of the line
  3. Parallel to XY
(b)Rotation method: a line's plan is swung about one end until parallel to XY. What stays unchanged?
  1. The length of its elevation
  2. The angle of its plan to XY
  3. The heights of its ends
(c)A line's plan is 40 mm long and its ends differ in height by 30 mm. What is its true length?
  1. 50 mm
  2. 35 mm
  3. 70 mm
Show the answers

(a) Parallel to the plan of the line

(b) The heights of its ends

(c) 50 mm

Your turn: Higher Level questions on True length & angles of lines.

Higher Level

Asked on 7 of the last 9 Higher Level papers, most recently in 2024. most years

Every paper, year by year

YearWhere it came up
2025Not asked
2024A3
2023B2
2022Not asked
2021B2
2019A1
2018A4, B3
2017A1, A4
2016A2

Links open the State Examinations Commission’s paper for that year.

More True length & angles of lines questions

True length & angles of lines, 3 marks

A line with a true length of 80 mm rises 40 mm. What is its inclination to the HP?

  1. 60°
  2. ≈26.6°
  3. 30°
Show the answer

30°

sin θ = rise ÷ true length = 40 ÷ 80 = 0.5, so θ = 30°. 26.6° comes from wrongly using tan.

True length & angles of lines, 3 marks

A line is 100 mm long and its plan is 60 mm long. How far apart in height are its ends?

  1. ≈116.6 mm
  2. 80 mm
  3. 40 mm
Show the answer

80 mm

True length, plan length and height difference form a right-angled triangle with the true length as hypotenuse: √(100² − 60²) = √6400 = 80 mm.

True length & angles of lines, 3 marks

In the trapezoid (rabatment) method for true length, about which line is the vertical trapezoid folded down?

  1. The line's plan
  2. The XY line
  3. The line's elevation
Show the answer

The line's plan

Perpendiculars equal to each end's height are set off from the plan and their tops joined to give the true length. Its angle with the plan is the inclination to the HP.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)