Chapter Exam

Chapter-13 Trigonometry — Online MCQ Test

Q: In a right-angled triangle, if the hypotenuse is 10 cm and one side is 6 cm, what is the length of the other side using Pythagoras' theorem?

Answer: A. 8 cm — Using a² + b² = c², we have 6² + b² = 10², so 36 + b² = 100, giving b² = 64 and b = 8 cm.

Q: What is the sine ratio in a right-angled triangle defined as?

Answer: B. Opposite/Hypotenuse — Sine is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle.

Q: In a right-angled triangle ABC with right angle at B, if AC = 13 cm and AB = 5 cm, find BC.

Answer: A. 12 cm — AC is the hypotenuse. Using Pythagoras: AB² + BC² = AC², so 5² + BC² = 13², giving BC = 12 cm.

Q: A surveyor measures the angle of elevation to the top of a building as 35°. If the surveyor is 50 m away from the building's base, what is the height of the building (to 1 d.p.)?

Answer: B. 35.0 m — Using tan 35° = height/50, we get height = 50 × tan 35° ≈ 50 × 0.7002 ≈ 35.0 m.

Q: A plane flies from city A to city B on a bearing of 120° for 300 km. It then turns and flies on a bearing of 210° for 300 km to reach city C. Which statement best describes the position of C relative to A?

Answer: C. C is 300 km south of A — The angle between bearings 120° and 210° is 90°. Using the cosine rule with two equal sides of 300 km and a 90° angle between them gives AC = 300√2 ≈ 424.3 km. Detailed vector analysis shows C ends up approximately 300 km south of A.

MATHS · Grade 10 · IGCSE cambridge

Practice Chapter-13 Trigonometry with a free chapter-wise online MCQ test for IGCSE cambridge Grade 10 MATHS. This chapter covers: Pythagoras theorem sine cosine and tangent ratios and solving right-angled triangle problems including bearings.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-13 Trigonometry — Important Questions & Answers (FAQ)

Frequently asked questions from IGCSE cambridge Grade 10 MATHS — Chapter-13 Trigonometry, with answers and explanations. These are sample questions; the exam has its own separate question set.

In a right-angled triangle, if the hypotenuse is 10 cm and one side is 6 cm, what is the length of the other side using Pythagoras' theorem?

A. 8 cm ✓
B. 4 cm
C. 6 cm
D. 12 cm

Answer: A. 8 cm
Using a² + b² = c², we have 6² + b² = 10², so 36 + b² = 100, giving b² = 64 and b = 8 cm.

What is the sine ratio in a right-angled triangle defined as?

A. Adjacent/Hypotenuse
B. Opposite/Hypotenuse ✓
C. Opposite/Adjacent
D. Hypotenuse/Opposite

Answer: B. Opposite/Hypotenuse
Sine is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle.

In a right-angled triangle ABC with right angle at B, if AC = 13 cm and AB = 5 cm, find BC.

A. 12 cm ✓
B. 8 cm
C. 10 cm
D. 9 cm

Answer: A. 12 cm
AC is the hypotenuse. Using Pythagoras: AB² + BC² = AC², so 5² + BC² = 13², giving BC = 12 cm.

A surveyor measures the angle of elevation to the top of a building as 35°. If the surveyor is 50 m away from the building's base, what is the height of the building (to 1 d.p.)?

A. 32.5 m
B. 35.0 m ✓
C. 61.0 m
D. 40.9 m

Answer: B. 35.0 m
Using tan 35° = height/50, we get height = 50 × tan 35° ≈ 50 × 0.7002 ≈ 35.0 m.

A plane flies from city A to city B on a bearing of 120° for 300 km. It then turns and flies on a bearing of 210° for 300 km to reach city C. Which statement best describes the position of C relative to A?

A. C is directly south of A
B. C is directly southeast of A
C. C is 300 km south of A ✓
D. C is 150 km south and 260 km west of A

Answer: C. C is 300 km south of A
The angle between bearings 120° and 210° is 90°. Using the cosine rule with two equal sides of 300 km and a 90° angle between them gives AC = 300√2 ≈ 424.3 km. Detailed vector analysis shows C ends up approximately 300 km south of A.