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Quiz Chapter 5: Trigonometric Ratios

10 questions · Form 3 Mathematics Bab 5: Trigonometric Ratios

Question 1 of 10Score: 0

What is the exact value of tan 45°?

Full Question List & Answer Key

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°?

  1. 0
  2. 12
  3. 1
  4. √3
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Answer: C

In an isosceles right-angled triangle with acute angles of 45°, opposite side = adjacent side, so tan 45° = 1.

2. 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.

  1. 1213
  2. 513
  3. 512
  4. 125
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Answer: B

Hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm. cos θ = Adjacent / Hypotenuse = 513.

3. Which side in a right-angled triangle is always opposite to the 90° angle and represents the longest side?

  1. Adjacent side
  2. Opposite side
  3. Hypotenuse
  4. Vertical side
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Answer: C

The hypotenuse is defined as the side directly opposite to the right angle (90°) and is always the longest side of a right-angled triangle.

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?

  1. 12 m
  2. 6 m
  3. 6.93 m
  4. 20.78 m
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Answer: C

tan 30° = Height / 12 => Height = 12 × tan 30° = 12 × (1/√3) = 12 × 0.5774 = 6.93 m.

5. If cos θ = 0.8 in a right-angled triangle with hypotenuse 15 cm, calculate the length of the adjacent side.

  1. 12 cm
  2. 9 cm
  3. 18.75 cm
  4. 10 cm
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Answer: A

cos θ = Adjacent / Hypotenuse => 0.8 = Adjacent / 15 => Adjacent = 0.8 × 15 = 12 cm.

6. In a right-angled triangle PQR where ∠Q = 90°, PQ = 8 cm and QR = 6 cm. What is tan ∠PRQ?

  1. 0.75
  2. 1.33
  3. 0.6
  4. 0.8
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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.

7. What is the exact value of cos 60°?

  1. 12
  2. √32
  3. 1/√2
  4. 1
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Answer: A

From the special angles ratio table, cos 60° = 12 = 0.5.

8. In triangle ABC, ∠B = 90°, AB = 9 cm, and AC = 15 cm. Find the value of sin ∠ACB.

  1. 0.6
  2. 0.8
  3. 0.75
  4. 1.25
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Answer: A

For angle ∠ACB, opposite side is AB (9 cm) and hypotenuse is AC (15 cm). sin ∠ACB = 915 = 0.6.

9. Convert 37.5° into degrees and minutes.

  1. 37° 50'
  2. 37° 30'
  3. 37° 05'
  4. 37° 15'
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Answer: B

0.5° × 60' = 30'. Thus, 37.5° = 37° 30'.

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?

  1. 3 m
  2. 5.2 m
  3. 4.5 m
  4. 2 m
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Answer: A

cos 60° = Distance / 6 => Distance = 6 × cos 60° = 6 × 0.5 = 3 m.

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