Lemmara logoLemmaraWorked solution

0580/33 May/Jun 2023, Question 7: Pythagoras' Theorem

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 15 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use angle facts, triangle properties, similarity and Pythagoras to find unknown angles, lengths and a perimeter from the given diagrams.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Give the mathematical name for an angle of 108°.

  1. 1108° is between 90° and 180°: obtuse

AnswerObtuse

Part (aii) · 1 mark

Find x, the angle on the straight line outside the triangle.

  1. 1Angles on a straight line add to 180°
  2. 2x = 180 − 108 = 72

Answer72

Part (aiii) · 1 mark

Find y, the third angle inside triangle ABC.

  1. 1Angles in a triangle add to 180°
  2. 2y = 180 − 46 − 108 = 26

Answer26

Part (b) · 1 mark

Demonstrate that the average of a triangle's three angles equals 60°.

  1. 1Angles in any triangle add to 180°
  2. 2Mean = 180/3 = 60°

Answer180/3

Part (c) · 3 marks

Find h, the hypotenuse of a right-angled triangle with side 8 cm and angle 35°.

  1. 1cos 35 = 8/h
  2. 2h = 8 ÷ cos 35
  3. 3= 9.766… ≈ 9.77

Answer9.77 or 9.766…

Part (di) · 2 marks

Given similar triangles ABC and PQR, find the length PR.

  1. 1Scale factor = 6.12 ÷ 1.36 = 4.5
  2. 2PR = 2.4 × 4.5 = 10.8 cm

Answer10.8

Part (dii) · 2 marks

Using the same similar triangles, find the length BC.

  1. 1BC = 7.92 ÷ 4.5
  2. 2= 1.76 cm

Answer1.76

Part (e) · 4 marks

Find the perimeter of a right-angled triangle with legs 24 cm and an unknown side, hypotenuse 26 cm.

  1. 1Third side² = 26² − 24² = 676 − 576 = 100
  2. 2Third side = √100 = 10 cm
  3. 3Perimeter = 24 + 26 + 10 = 60 cm

Answer60

Stuck on a step? Read the free lesson: Pythagoras' Theorem

Practise more pythagoras' theorem questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on pythagoras' theorem

Also searched as: 0580/33/M/J/23 · 0580_s23_qp_33 · 0580 s23 33 · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.