10 questions · Form 3 Mathematics Bab 5: Trigonometric Ratios
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the exact value of tan 45°?
Answer: C
In an isosceles right-angled triangle with acute angles of 45°, opposite side = adjacent side, so tan 45° = 1.
2. In a right-angled triangle, if the side opposite to angle θ is 6 cm and the hypotenuse is 10 cm, what is sin θ?
Answer: B
sin θ = Opposite / Hypotenuse = 610 = 0.6.
3. If cos θ = 0.5, what is the value of tan θ?
Answer: C
cos θ = 0.5 implies θ = 60°. tan 60° = √3 ≈ 1.732.
4. A vertical flagpole casts a shadow of 12 m on horizontal ground. The angle of elevation of the sun is 30°. What is the height of the flagpole?
Answer: C
tan 30° = Height / 12 => Height = 12 × tan 30° = 12 × (1/√3) = 12 × 0.5774 = 6.93 m.
5. Convert 42° 18' into decimal degrees.
Answer: B
18' / 60 = 0.3°. Therefore, 42° 18' = 42.3°.
6. Given a right-angled triangle with adjacent side = 5 cm and opposite side = 12 cm, calculate the hypotenuse length using Pythagoras theorem, then find cos θ.
Answer: B
Hypotenuse = √5² + 12² = √25 + 144 = √169 = 13 cm. cos θ = Adjacent / Hypotenuse = 513.
7. Calculate the value of sin 30° + cos 60°.
Answer: A
sin 30° = 12 and cos 60° = 12. Therefore, 12 + 12 = 1.
8. If cos θ = 0.8 in a right-angled triangle with hypotenuse 15 cm, calculate the length of the adjacent side.
Answer: A
cos θ = Adjacent / Hypotenuse => 0.8 = Adjacent / 15 => Adjacent = 0.8 × 15 = 12 cm.
9. What is the exact value of sin 60°?
Answer: C
From the special trigonometric ratios table, sin 60° = √32.
10. A ladder resting against a vertical wall makes an angle of 60° with the ground. If the ladder is 6 m long, how far is the foot of the ladder from the wall?
Answer: A
cos 60° = Distance / 6 => Distance = 6 × cos 60° = 6 × 0.5 = 3 m.