In IGCSE Year 10, trigonometry uses sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent, with standard values sin 30° = 0.5, cos 60° = 0.5 and tan 45° = 1. The 20 questions cover the cosine rule and angles of elevation, and the answer key is on this page.
Key Takeaways
sin θ = opposite ÷ hypotenuse and cos θ = adjacent ÷ hypotenuse in any right-angled triangle (Q1).
Standard values to remember: tan 45° = 1, sin 30° = 0.5, cos 60° = 0.5 (Q2–Q4).
The cosine rule is the right tool when you know two sides and the included angle (Q6, Q20).
Given values such as sin 60° = 0.866, sin 50° = 0.766 and tan 30° = 0.577 are supplied for the word problems (Q13, Q15, Q17).
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.In a right-angled triangle, sin θ equals which ratio?
5.In a right-angled triangle, the side opposite a 35° angle is 6 cm and the hypotenuse is 10 cm. What is the value of sin 35° for this triangle?
(a) 0.6(b) 0.8(c) 1.67(d) 0.75
6.The cosine rule is most useful when you know which information?
(a) two angles and any side(b) two sides and the included angle(c) only one side(d) one angle and one side
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State the value of cos 0°.
8.Write sin 40° correct to 2 decimal places.
9.A right-angled triangle has sides 5, 12 and 13 with hypotenuse 13. Find the sine of the angle opposite the side of length 5.
10.The hypotenuse of a right-angled triangle is 10 cm and one angle is 30°. Find the length of the side opposite this angle.
11.State the value of tan 0°.
12.In a right-angled triangle, cos A = 0.8 and the hypotenuse is 10 cm. Find the length of the adjacent side.
13.A ladder 5 m long makes an angle of 60° with the ground. Find the height it reaches, using sin 60° = 0.866.
14.State the sine rule for a triangle with angles A, B, C and opposite sides a, b, c.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A kite string is 20 m long and makes an angle of 50° with the horizontal. Find the height of the kite, using sin 50° = 0.766.
16.A ramp rises 2 m over a horizontal distance of 5 m. Find the angle of elevation, given that tan θ = 0.4 and tan 21.8° = 0.4.
17.From the top of a 30 m tower, the angle of depression to a car is 30°. Find the horizontal distance from the car to the base of the tower, using tan 30° = 0.577.
18.A ship sails 12 km north then 5 km east. Find the straight-line distance from its starting point.
19.The angle of elevation of the top of a building is 45° from a point 40 m away. Find the height of the building.
20.In triangle ABC, AB = 8 cm, AC = 5 cm and angle A = 60°. Find BC using the cosine rule, with cos 60° = 0.5.
Answer Key
1. b) opposite ÷ hypotenuse
2. c) 1
3. d) 0.5
4. a) 0.5
5. a) 0.6
6. b) two sides and the included angle
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the value of tan 45°?
tan 45° = 1. It is option (c) in this worksheet (Q2).
What is the value of sin 30°?
sin 30° = 0.5. It is option (d) in this worksheet (Q3).
What does sin equal in a right-angled triangle?
sin θ = opposite ÷ hypotenuse. It is option (b) in this worksheet (Q1).
When is the cosine rule most useful?
When you know two sides and the included angle, as in Q6 and Q20 here.
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