O Level / IGCSE Mathematics chapter 6: Trigonometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

36 exam-style questions on Trigonometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

36 questions · 4 topics · 10 per test

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What chapter 6 covers

Ten Trigonometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. An equilateral triangle has sides of 8 cm. Find its perpendicular height, correct to 3 significant figures.

  1. A
    8.94 cm
  2. B
    5.66 cm
  3. C
    4.00 cm
  4. D
    6.93 cm
Show answer

Answer: D. The height bisects the base into 4 cm and 4 cm: h = √(82 − 42) = √48 = 6.93 cm. Adding the squares gives √80 = 8.94.

2. In triangle PQR, PQ = 10 cm, PR = 12 cm and angle QPR = 150°. Find the area of the triangle.

  1. A
    60 cm2
  2. B
    30 cm2
  3. C
    52.0 cm2
  4. D
    120 cm2
Show answer

Answer: B. Area = ½ × 10 × 12 × sin 150° = 60 × 0.5 = 30 cm2. sin 150° = sin 30° = 0.5; the obtuse angle still gives a positive area.

3. The diagonal of a rectangle is 12 cm long and makes an angle of 30° with the longer side. Find the area of the rectangle, correct to 3 significant figures.

  1. A
    62.4 cm2
  2. B
    36.0 cm2
  3. C
    31.2 cm2
  4. D
    72.0 cm2
Show answer

Answer: A. Longer side = 12 cos 30° = 10.39 cm and shorter side = 12 sin 30° = 6 cm. Area = 10.39 × 6 = 62.4 cm2. 31.2 is only the triangle on one side of the diagonal.

4. An isosceles triangle has two sides of 13 cm and a base of 10 cm. Find its area.

  1. A
    65 cm2
  2. B
    120 cm2
  3. C
    60 cm2
  4. D
    30 cm2
Show answer

Answer: C. The perpendicular from the apex bisects the base into 5 cm and 5 cm. Height = √(132 − 52) = √144 = 12 cm. Area = ½ × 10 × 12 = 60 cm2.

5. An isosceles triangle has two sides of 10 cm with an angle of 40° between them. Find the length of the base, correct to 3 significant figures.

  1. A
    9.40 cm
  2. B
    6.84 cm
  3. C
    12.9 cm
  4. D
    3.42 cm
Show answer

Answer: B. The line of symmetry splits the triangle into two right-angled triangles with angle 20° at the top. Half the base = 10 × sin 20° = 3.42, so the base is 6.84 cm. 9.40 is the height.

6. A right-angled triangle has a hypotenuse of 17 cm and one shorter side of 8 cm. Find the length of the third side.

  1. A
    25 cm
  2. B
    15 cm
  3. C
    9 cm
  4. D
    18.8 cm
Show answer

Answer: B. Third side = √(172 − 82) = √(289 − 64) = √225 = 15 cm. Adding the squares gives 18.8, which would be longer than the hypotenuse.

7. A ladder 5 m long leans against a vertical wall and makes an angle of 70° with the horizontal ground. How far up the wall does it reach, correct to 3 significant figures?

  1. A
    1.71 m
  2. B
    13.7 m
  3. C
    5.32 m
  4. D
    4.70 m
Show answer

Answer: D. The ladder is the hypotenuse and the height is opposite 70°: 5 × sin 70° = 4.70 m. 1.71 m is the distance of the foot from the wall.

8. A rectangle has a diagonal of 25 cm and a width of 7 cm. Find its length.

  1. A
    32 cm
  2. B
    26 cm
  3. C
    18 cm
  4. D
    24 cm
Show answer

Answer: D. The diagonal is the hypotenuse: length = √(252 − 72) = √(625 − 49) = √576 = 24 cm.

9. The perpendicular distance from a point P to a straight line L is 7 cm. A is a point on L, but not at the foot of the perpendicular. Which of these could be the length of PA?

  1. A
    9 cm
  2. B
    6 cm
  3. C
    7 cm
  4. D
    5 cm
Show answer

Answer: A. The perpendicular distance is the shortest distance from P to the line, so any other point A on L is more than 7 cm from P. Only 9 cm is possible.

10. A boat sails 12 km from a harbour on a bearing of 050°. How far east of the harbour is it, correct to 3 significant figures?

  1. A
    7.71 km
  2. B
    15.7 km
  3. C
    14.3 km
  4. D
    9.19 km
Show answer

Answer: D. The bearing angle 50° is measured from north, so the east distance is opposite it: 12 × sin 50° = 9.19 km. 12 × cos 50° = 7.71 km is the distance north.

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Ways to practise this chapter

Trigonometry: questions students ask

How many Trigonometry MCQs are there?

36, each with the answer and a short explanation, across 4 topics: Pythagoras’ theorem, Right-angled triangles, Non-right-angled triangles, Pythagoras’ theorem and trigonometry. Every chapter test draws ten of them, so you can take it many times.

Is the O Level / IGCSE Mathematics chapter 6 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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