Trigonometric Ratios Quiz

Grade 10 · Math · Quiz

Test your knowledge of SOH-CAH-TOA, trig ratios, and right triangle problem solving.

Questions

1. What is tan(45°)?

   1. 0
   2. 1/2
   3. 1
   4. √3
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   Answer: 1

   tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1. Also: in a 45-45-90 triangle, the legs are equal so opp/adj = 1.

2. cos(θ) = Adjacent / ___.

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   Answer: Hypotenuse

   CAH: Cosine = Adjacent/Hypotenuse.

3. In a right triangle with legs 3 and 4 and hypotenuse 5, what is sin of the angle opposite the side of length 3?

   1. 3/5
   2. 4/5
   3. 3/4
   4. 5/3
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   Answer: 3/5

   sin = opp/hyp = 3/5. The angle is opposite the side of length 3, and the hypotenuse is 5.

4. tan(90°) is defined and equals 1.

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   Answer: False

   tan(90°) is undefined because the adjacent side has length 0 (division by zero). cos(90°) = 0, so tan = sin/cos = 1/0 = undefined.

5. A ladder leans against a wall, making a 60° angle with the ground. If the ladder is 10m long, how high does it reach?

   1. 5 m
   2. 5√3 m
   3. 10√3 m
   4. √3 m
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   Answer: 5√3 m

   sin(60°) = opp/hyp → (√3/2) = opp/10 → opp = 10·(√3/2) = 5√3 ≈ 8.66m.

6. The inverse trig function used to find an angle when given opposite and adjacent sides is ___⁻¹.

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   Answer: tan

   tan = opp/adj, so tan⁻¹(opp/adj) gives the angle. Use tan⁻¹ when you have the two legs.

7. sin(30°) equals:

   1. √3/2
   2. 1/2
   3. √2/2
   4. 1
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   Answer: 1/2

   sin(30°) = 1/2 = 0.5. Memorize the 30-60-90 triangle: sides are 1, √3, 2.

8. In a right triangle, sin(θ) = cos(90° - θ) for any acute angle θ.

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   Answer: True

   This is the co-function identity: sin and cos are complementary functions. sin(θ) = cos(90°-θ) always holds for acute angles.

9. If tan(θ) = 5/12, what is sin(θ) in the corresponding right triangle?

   1. 5/13
   2. 12/13
   3. 5/12
   4. 12/5
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   Answer: 5/13

   tan(θ)=5/12 means opp=5, adj=12. Hypotenuse by Pythagorean: √(25+144)=√169=13. sin(θ)=5/13.

10. For any angle θ in a right triangle, sin²(θ) + cos²(θ) = 1.

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    Answer: True

    The Pythagorean identity sin²θ + cos²θ = 1 is one of the most fundamental identities in trigonometry, derived directly from a² + b² = c² in a unit circle.

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