10 questions · Form 3 Mathematics Bab 5: Trigonometric Ratios
If cos θ = 0.8 in a right-angled triangle with hypotenuse 15 cm, calculate the length of the adjacent side.
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. 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.
2. 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.
3. What is the exact value of cos 60°?
Answer: A
From the special angles ratio table, cos 60° = 12 = 0.5.
4. Calculate the value of sin 30° + cos 60°.
Answer: A
sin 30° = 12 and cos 60° = 12. Therefore, 12 + 12 = 1.
5. In triangle ABC, ∠B = 90°, AB = 9 cm, and AC = 15 cm. Find the value of sin ∠ACB.
Answer: A
For angle ∠ACB, opposite side is AB (9 cm) and hypotenuse is AC (15 cm). sin ∠ACB = 915 = 0.6.
6. 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.
7. In a right-angled triangle PQR where ∠Q = 90°, PQ = 8 cm and QR = 6 cm. What is tan ∠PRQ?
Answer: B
For angle ∠PRQ, the opposite side is PQ (8 cm) and the adjacent side is QR (6 cm). tan ∠PRQ = 86 = 1.33.
8. Convert 37.5° into degrees and minutes.
Answer: B
0.5° × 60' = 30'. Thus, 37.5° = 37° 30'.
9. If sin θ = 0.5, what is the value of acute angle θ?
Answer: C
θ = sin⁻¹(0.5) = 30°.
10. 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.