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

10.5

2. $Math 112. 06$

3. 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

None of these

Circum – Center

Ex – center

In – center

4. a/sina = b/sinβ – c/sinϒ is law of

Cosine

Sine

Tangent

Cotangent

5. Law of cosine is

c²=a²+b² – 2ab Cos y

a² + 2ab cos a = b² + c²

All of these

Cos a = b²+c²–a²/2bc

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

External bisectors of A, B and C

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

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

4300.85

190

4860.8

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

53°7’

180°

90°

9. r₃ =

s tan β/2

s tan ϒ/2

s tan a

s tan a/2

10. 1/ab + 1/bc + 1/ca =

2rR

1/2rR

r/2R

R/2r

11. √rr₁r₂r₃ = ?

½ bc sin β

sin a

∆

∆/abc

12. R =

c/2sina

b/sinβ

a/2sinβ

c/2sinϒ

13. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₃

r₂

r₁

14. 4R cos ½ a sin ½ β cos ½ ϒ =

r₁

r₃

r₂

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

None of these

Angle of depression

Right angle

Angle of elevation

16. Which one is true?

a²+b²+c² = 2abcos a

b² = a²+c²+2ac cos β

cos a = a²+b²+c²/2ab

a²=b²+c² - 2bc cos a

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

Right angle

Angle of depression

Angle of elevation

Constant angle

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

a²sina/2sinβ sinϒ

a²sinβ sinϒ/2 sin a

c²sina/2sinβ sinϒ

b²sina/2sinβ sinϒ

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

None of these

Altitude

Elevation

Depression

20. Sum of opposite angles of a cyclic quadrilateral is

270°

360°

180°

120°

21. Pythagorous theorem is solve

Rectangles

Oblique triangles

Right – triangles

None of these

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

6000 square units

9000 square units

5000 square units

7000 square units

23. $Math 112. 01$

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

a+b+c/4

a+b+c/3

a+b+c/2

a+b+c

25. E – radius corresponding to

26. 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)

27. Number of elements of triangle is known as

28. Hero’s formula is used to calculate

29. In ∆ ABC, a²+b²-c²/2ab is

30. $Math 112. 04$

31. Circum radius of a circle is denoted by

r₂

32. 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

225 m

100 m

377 m

477 m

33. $Math 112. 02$

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

40°

50°

45°

550°

35. 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 elevation

Constant angle

Right angle

Angle of depression

36. r₃ =

s – a/∆

∆/s – b

∆/s – c

∆/s – a

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

1001

721325

13078800

12895

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

B = 113.3, c = 143.8

B = 143.8, c = 113.3

B = 43.8, c = 13.3

B = 13.3, c = 43.8

39. $Math 112. 05$

40. cot a/2 =

$Math 112. 03$

41. 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

6(1 + √3)m

3(1 + √3)m

None of these

(1 + √3)m

42. 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

15 m

10 m

None of these

20 m

43. 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 2/9

tan⁻¹ 5/9

tan⁻¹ 1/9

tan⁻¹ 4/9

44. 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

60°

None of these

30°

45°

45. R =

c/2sinϒ

a/2sinϒ

a/2sina

a/2sinβ

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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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