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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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).

100√3

150(√3+1)

100/√3

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

Right angle

None of these

Angle of elevation

Angle of depression

3. 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

Right angle

Angle of depression

Constant angle

Angle of elevation

4. R =

a/2sinβ

c/2sina

b/sinβ

c/2sinϒ

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

External bisector of A and B and internal bisector of C

External bisectors of B and C and internal bisectors of A

External bisectors of A and C and internal bisector of B

External bisectors of A, B and C

6. Circum radius of a circle is denoted by

r₂

7. 1/ab + 1/bc + 1/ca =

1/2rR

2rR

r/2R

R/2r

8. cot a/2 =

$Math 112. 03$

9. r₃ =

s tan β/2

s tan ϒ/2

s tan a

s tan a/2

10. $Math 112. 02$

11. Which one is true?

b² = a²+c²+2ac cos β

a²+b²+c² = 2abcos a

a²=b²+c² - 2bc cos a

cos a = a²+b²+c²/2ab

12. Pythagorous theorem is solve

Rectangles

Oblique triangles

None of these

Right – triangles

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

50°

550°

45°

40°

14. Hero’s formula is used to calculate

Angles of ∆

None of these

Sides of ∆

Area of ∆

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

45°

60°

30°

None of these

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

a+b+c/3

a+b+c/2

a+b+c/4

a+b+c

17. R =

a/2sina

a/2sinβ

a/2sinϒ

c/2sinϒ

18. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₂

r₁

r₃

19. $Math 112. 05$

20. $Math 112. 01$

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

90°

53°7’

180°

22. √rr₁r₂r₃ = ?

sin a

∆

∆/abc

½ bc sin β

23. 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

(1 + √3)m

3(1 + √3)m

6(1 + √3)m

None of these

24. 4R cos ½ a sin ½ β cos ½ ϒ =

r₂

r₁

r₃

25. 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

Ex – center

None of these

Circum – Center

Page 2 of 2

26. 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

225 m

100 m

377 m

27. E – radius corresponding to

28. $Math 112. 04$

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

4300.85

4860.8

190

30. 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

31. In ∆ ABC, a²+b²-c²/2ab is

Cos a

None of these

Cos β

Cos ϒ

32. Sum of opposite angles of a cyclic quadrilateral is

270°

120°

180°

360°

33. 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 4/9

tan⁻¹ 2/9

tan⁻¹ 5/9

tan⁻¹ 1/9

34. Number of elements of triangle is known as

Trigonometry

Vectors

None of these

Algebra

35. r₃ =

∆/s – a

∆/s – c

s – a/∆

∆/s – b

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

1001

721325

12895

13078800

37. Law of cosine is

Cos a = b²+c²–a²/2bc

All of these

a² + 2ab cos a = b² + c²

c²=a²+b² – 2ab Cos y

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

B = 43.8, c = 13.3

B = 143.8, c = 113.3

B = 113.3, c = 143.8

B = 13.3, c = 43.8

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

5000 square units

7000 square units

6000 square units

9000 square units

40. $Math 112. 06$

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

10.5

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

Sine

Tangent

Cotangent

Cosine

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

Angle of elevation

Angle of depression

Right angle

Constant angle

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

c²sina/2sinβ sinϒ

a²sinβ sinϒ/2 sin a

a²sina/2sinβ sinϒ

b²sina/2sinβ sinϒ

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

Elevation

Altitude

None of these

Depression

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Mustansar KhanLast Updated: October 15, 2025

Important Math Application of Trigonometry Question and Answer

Math Application of Trigonometry Practice Test Online With Explanation

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