0580/32 Feb/Mar 2024, Question 3: The Tangent Ratio

Part (a) · 2 marks

Using only a ruler and compasses, draw triangle DEF with DE = 6 cm and DF = 4.8 cm, keeping all construction arcs visible.

1. 1Open compasses to 6 cm, centre E, draw an arc above EF
2. 2Open compasses to 4.8 cm, centre F, draw an arc crossing the first arc
3. 3The crossing point is D; join DE and DF with a ruler

AnswerCorrect triangle drawn with construction arcs

Part (bi) · 1 mark

From the grid, name the triangle that is exactly the same shape and size as triangle T.

1. 1G has the same shape and size as T (rotated)
2. 2G

AnswerG

Part (bii) · 1 mark

From the grid, name the triangle that has the same shape as T but a different size.

1. 1F is an enlargement of T, same angles but larger
2. 2F

AnswerF

Part (ci) · 3 marks

For the isosceles triangle with base 7 cm and base angles 62°, prove that the perpendicular height h is 6.58 cm to 3 significant figures.

1. 1The height bisects the base: half base = 3.5 cm
2. 2tan 62° = h ÷ 3.5
3. 3h = 3.5 × tan 62° = 6.582…
4. 4= 6.58 cm to 3 s.f.

Answerh = 7/2 × tan 62 = 6.582 to 6.583

Part (cii) · 3 marks

Work out the area of the isosceles triangle, giving the correct units.

1. 1Area = 1/2 × 7 × 6.58
2. 2= 23.03 = 23.0
3. 3Units: cm²

Answer23.0 or 23.03 to 23.04, cm²

Part (ciii) · 3 marks

Using the arrangement of triangles meeting at centre O, show that a regular polygon cannot be formed.

1. 1Angle at O = 180 − 2 × 62 = 56°
2. 2Number of triangles = 360 ÷ 56 = 6.43…
3. 36.43… is not a whole number, so the triangles cannot fit exactly round O
4. 4So Kalpit cannot make a regular polygon

Answer360 ÷ (180 − 2 × 62) = 6.4…, which is not an integer

More past-paper questions on the tangent ratio

• 0580/33 May/Jun 2026 Q25 · 5 marks
• 0580/42 May/Jun 2026 Q11 · 2 marks
• 0580/32 Oct/Nov 2025 Q26 · 2 marks
• 0580/11 May/Jun 2023 Q22 · 2 marks
• 0580/31 Oct/Nov 2023 Q10 · 9 marks
• 0580/31 May/Jun 2021 Q6 · 14 marks