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Mathematics Application of Trigonometry Online Test

Mustansar KhanLast Updated: October 15, 2025

Important Math Application of Trigonometry Question and Answer

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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Math Application of Trigonometry Practice Test Online With Explanation

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Page 1 of 2

2. In ∆ ABC, a²+b²-c²/2ab is

Cos a

Cos β

Cos ϒ

None of these

3. Circum radius of a circle is denoted by

r₂

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

External bisectors of A, B and C

External bisectors of B and C and internal bisectors of A

External bisector of A and B and internal bisector of C

External bisectors of A and C and internal bisector of B

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

9000 square units

6000 square units

7000 square units

5000 square units

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

Right angle

None of these

Angle of elevation

Angle of depression

8. 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

None of these

45°

60°

30°

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

10.5

10. 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

10 m

15 m

None of these

20 m

11.

12. R =

a/2sinβ

b/sinβ

c/2sinϒ

c/2sina

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

Cotangent

Cosine

Tangent

Sine

14. r₃ =

s tan a/2

s tan ϒ/2

s tan a

s tan β/2

15. 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

Angle of depression

Right angle

Constant angle

Angle of elevation

16. Hero’s formula is used to calculate

Sides of ∆

Angles of ∆

Area of ∆

None of these

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

1001

12895

721325

13078800

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

4300.85

4860.8

190

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

Angle of depression

Right angle

Angle of elevation

Constant angle

20. 1/ab + 1/bc + 1/ca =

R/2r

1/2rR

2rR

r/2R

21. 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).

100√3

100/√3

150(√3+1)

22. Law of cosine is

All of these

a² + 2ab cos a = b² + c²

Cos a = b²+c²–a²/2bc

c²=a²+b² – 2ab Cos y

23. E – radius corresponding to

25. Which one is true?

a²+b²+c² = 2abcos a

cos a = a²+b²+c²/2ab

b² = a²+c²+2ac cos β

a²=b²+c² - 2bc cos a

Page 2 of 2

26. 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

None of these

3(1 + √3)m

6(1 + √3)m

(1 + √3)m

27.

28. Sum of opposite angles of a cyclic quadrilateral is

360°

180°

270°

120°

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

a+b+c/2

a+b+c

a+b+c/4

a+b+c/3

30. 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 =

tan⁻¹ 1/9

tan⁻¹ 5/9

tan⁻¹ 4/9

tan⁻¹ 2/9

31. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₁

r₂

r₃

32. √rr₁r₂r₃ = ?

∆

½ bc sin β

∆/abc

sin a

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

None of these

Altitude

Depression

Elevation

34.

35. r₃ =

∆/s – b

∆/s – a

s – a/∆

∆/s – c

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

90°

180°

53°7’

37. 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

477 m

100 m

377 m

225 m

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

550°

40°

45°

50°

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

B = 13.3, c = 43.8

B = 43.8, c = 13.3

B = 113.3, c = 143.8

B = 143.8, c = 113.3

40. Number of elements of triangle is known as

Trigonometry

None of these

Algebra

Vectors

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

a²sinβ sinϒ/2 sin a

b²sina/2sinβ sinϒ

a²sina/2sinβ sinϒ

c²sina/2sinβ sinϒ

42. Pythagorous theorem is solve

Oblique triangles

Right – triangles

Rectangles

None of these

43. R =

a/2sinϒ

a/2sinβ

c/2sinϒ

a/2sina

44. 4R cos ½ a sin ½ β cos ½ ϒ =

r₁

r₂

r₃

45. 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

In – center

Circum – Center

None of these

Ex – center

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Mustansar KhanLast Updated: October 15, 2025

Mathematics Application of Trigonometry Online Test

Important Math Application of Trigonometry Question and Answer

Math Application of Trigonometry Practice Test Online With Explanation

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