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**Trigonometry Online MCQs with Answers**

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**Trigonometry Online MCQs**

1. The base of a triangle is 48 sqrt(3) cm and two angles at the base are 30 degree and 60 degree respectively. Then find the altitude of the triangle

40

43

36

50

None of these

Correct Ans: 36

2. If θ be acute angle and cosθ = 15/17, then the value of cot (90° – θ) is

2√8/15

8/15

√2/7

8√7/17

None of these

Correct Ans: 8/15

3. If cotα = 3, then the value of (sin^{3}α + cos^{3}α)/cosα is ?

25/27

14/15

9

11/15

None of these

Correct Ans: 14/15

4. If 7sinÎ± = 24cosÎ±; 0 < Î± < Ï€/2, then the value of 14tanÎ± – 75cosÎ± – 7secÎ± is equal to

3

4

1

2

None of these

Correct Ans: 2

5. Provided sin (A ““ B) = sinA cosB ““ cosA sinB, then sin 15Â° will be

√3/2√2

(√3 – 1)/2√2

(√3 – 1)/√2

(√3 – 1)/2

None of these

Correct Ans: (√3 – 1)/2√2

6. The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then, in metre, the height of the building is.

h cotx/(cotx – coty)

h coty/(cotx + coty)

h cotx/(cotx + coty)

h coty/(cotx – coty)

None of these

Correct Ans: h cotx/(cotx – coty)

7. If sin 21Â° = x/y, then sec 21Â° – sin 69Â° is equal to

x^{2}/y√(y^{2} – x^{2})

y^{2}/x√(y^{2} – x^{2})

x^{2}/y√(x^{2} – y^{2})

y^{2}/x√(x^{2} – y^{2})

None of these

Correct Ans: x^{2}/y√(y^{2} – x^{2})

8. If xsin^{3}θ + ycos^{3}θ = sinθ cosθ and x sinθ – y cosθ = 0, then the value of x^{2} + y^{2} equals

1

1/2

3/2

2

None of these

Correct Ans: 1

9. A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation of 30° and after 2 minutes, he observes the same bird in the south at an angle of elevation of 60°. If the bird flies all along in a straight line at a height of m, then its speed in km/h is

4.5

3

9

6

None of these

Correct Ans: 6

10. If sin(x + y)/sin(x – y) = (a + b)/(a – b), then the value of tanx/tany is

a/b

b/a

ab

(a – b)/(a + b)

None of these

Correct Ans: a/b

11. If sin3Î¸ sec2Î¸ = 1, then what is the value of (3tan^{2} (5Î¸/2) ““ 1)?

0

1

2

3

None of these

Correct Ans: 2

12. Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30Â° and 60Â° respectively. The distance between the persons is

173.2 m

100 m

157.7 m

273.2 m

None of these

Correct Ans: 173.2 m

13. 2 – cos^{2}θ = 3sinθcosθ, sinθ ≠ cosθ then tanθ is

1/2

0

2/3

1/3

None of these

Correct Ans: 1/2

14. An person 1.8m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. Find height of the tower is?

21.8m

23.8m

21.6m

24.8m

None of these

Correct Ans: 21.8m

15. Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

(5√3)/2

5√3

Both a and b

√3

None of these

Correct Ans: Both a and b

16. If cos θ + sec θ = 2, the value of cos^{6} θ + sec^{6} θ is

4

8

1

2

None of these

Correct Ans: 2

17. If x = cosecðœƒ- sinðœƒ and y = secðœƒ – cosðœƒ, then the relation between x and y is

x^{2} + y^{2} + 3 = 1

x^{2}y^{2}(x^{2} + y^{2} + 3) = 1

x^{2}(x^{2} + y^{2} – 5) = 1

y^{2}(x^{2} + y^{2} – 5) = 1

None of these

Correct Ans: x^{2}y^{2}(x^{2} + y^{2} + 3) = 1

18. If is an acute angle and cosðœƒ = 15/17, then the value of cot (90º – ðœƒ) is

2√8/15

8/15

√2/17

8√2/17

None of these

Correct Ans: 8/15

19. If 0°<θ<90°

2sinÂ²θ + 3cosθ = 3, then the value of θ is ?

30°

60°

45°

75°

None of these

Correct Ans: 60°

20. What is the value of (2 + tan 60º) ?

3

2/√3

4/√3

2 + √3

None of these

Correct Ans: 2 + √3