Mathematics Application of Trigonometry Online Test

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Question 1

1. An airplane flying at a height of 300 meters above the ground passes vertically above another place at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Then the height of the lower plane from the ground is (in meters).

Answer

150(√3+1)

Question 2

2. √rr₁r₂r₃ = ?

Answer

½ bc sin β

Question 3

3. R =

Question 4

4. The area of a triangle with a = 300, b = 120, ϒ = 150° is

Answer

9000 square units

Answer

5000 square units

Answer

6000 square units

Answer

7000 square units

Question 5

5. A tree of 8 m high has the shadow 6m in length, the angle of elevation of the sun at that moment is

Question 6

6. If for a ∆ ABC, a = 7, b = 9, c = 7, then ϒ = ?

Question 7

7. If ∆ is the area of a triangle ABC, then ∆ =

Answer

c²sina/2sinβ sinϒ

Answer

a²sina/2sinβ sinϒ

Answer

a²sinβ sinϒ/2 sin a

Answer

b²sina/2sinβ sinϒ

Question 8

8. If β = 52°,ϒ = 89°35’, a = 89.35 in a triangle ABC, then

Answer

B = 43.8, c = 13.3

Answer

B = 13.3, c = 43.8

Answer

B = 113.3, c = 143.8

Answer

B = 143.8, c = 113.3

Question 9

9. Hero’s formula is used to calculate

Answer

Area of ∆

Answer

Angles of ∆

Answer

None of these

Answer

Sides of ∆

Question 10

10. Circum radius of a circle is denoted by

Question 11

11. If a = 315, b = 346, c = 120 then product of the three sides = ?

Question 12

12. 4R cos ½ a sin ½ β cos ½ ϒ =

Question 13

13. The angles of elevation of the top of a tower at the top and the foot of a pole of height 10 m are 30° and 60° respectively. The height of the tower is

Answer

None of these

Question 14

14. 1/ab + 1/bc + 1/ca =

Question 15

15. If a flagstaff 6 meters high placed on the top of a tower throws a shadow of 2√3 meters along the ground then the angle (in degrees) that the sun makes with the ground is

Answer

None of these

Question 16

16. If you are looking someone on the ground from the op a hill, the angle formed is the

Answer

Constant angle

Answer

Angle of depression

Answer

Right angle

Answer

Angle of elevation

Question 17

17. r₃ =

Answer

s tan ϒ/2

Answer

s tan β/2

Question 18

18.

Question 19

19. The angle above horizontal line and the line of sight is an angle of

Answer

Depression

Answer

None of these

Question 20

20. R =

Question 21

21. Sum of opposite angles of a cyclic quadrilateral is

Question 22

22. If a = 13, b = 14, c = 15, then r₂ =

Question 23

23. The x – center with respect to the vertex B is the point of intersection of the

Answer

External bisectors of B and C and internal bisectors of A

Answer

External bisector of A and B and internal bisector of C

Answer

External bisectors of A and C and internal bisector of B

Answer

External bisectors of A, B and C

Question 24

24. Which one is true?

Answer

a²+b²+c² = 2abcos a

Answer

cos a = a²+b²+c²/2ab

Answer

b² = a²+c²+2ac cos β

Answer

a²=b²+c² - 2bc cos a

Question 25

25. For a triangle, ∆ = 888 and s = 24, then radius of in circle is

Question 26

26. Law of cosine is

Answer

All of these

Answer

a² + 2ab cos a = b² + c²

Answer

c²=a²+b² – 2ab Cos y

Answer

Cos a = b²+c²–a²/2bc

Question 27

27.

Question 28

28.

Question 29

29. An angle below the horizontal line and line of sight is called

Answer

Angle of elevation

Answer

Angle of depression

Answer

None of these

Answer

Right angle

Question 30

30. The angle AOP which the ray from an observer’s eye at O to an object at P at a higher r level makes with horizontal ray OA through O is called the

Answer

Constant angle

Answer

Right angle

Answer

Angle of elevation

Answer

Angle of depression

Question 31

31.

Question 32

32.

Question 33

33. Pythagorous theorem is solve

Answer

Right – triangles

Answer

None of these

Answer

Rectangles

Answer

Oblique triangles

Question 34

34. E – radius corresponding to

Answer

∆/s – a

Answer

∆/s – c

Answer

∆/s – b

Question 35

35. At the top of a cliff 80 m high, the angle of depression of a boat is 12°. The distance of the boat from the cliff is

Question 36

36. Number of elements of triangle is known as

Answer

Trigonometry

Answer

None of these

Question 37

37. AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angle β at P. If AP:AB = 2:1 then β =

Answer

tan⁻¹ 1/9

Answer

tan⁻¹ 5/9

Answer

tan⁻¹ 2/9

Answer

tan⁻¹ 4/9

Question 38

38. In ∆ ABC, a²+b²-c²/2ab is

Answer

None of these

Question 39

39. cot a/2 =

Question 40

40. A man of height 6 ft observes the top of a tower and the foot of the tower at angles of 45° and 30° of elevation and depression respectively. The height of the towers is

Answer

None of these

Answer

(1 + √3)m

Answer

3(1 + √3)m

Answer

6(1 + √3)m

Question 41

41. If a, b, c are the sides of the triangle ABC, then s =

Question 42

42. a/sina = b/sinβ – c/sinϒ is law of

Question 43

43. r₃ =

Answer

∆/s – a

Answer

∆/s – c

Answer

s – a/∆

Answer

∆/s – b

Question 44

44. The point of intersection of the internal bisector of one angle and external bisectors of the other two angles of a triangle is known as

Answer

None of these

Answer

Circum – Center

Answer

Ex – center

Answer

In – center

Question 45

45. 4 R sin a/2 sin β/2 sin ϒ/2 =

Question 46

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Total Questions:	45
Time Allowed:	20 Minutes
Total Marks:	45
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Important Math Application of Trigonometry Question and Answer

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