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ECAT Mathematics Application of Trigonometry Online Test

Mustansar KhanLast Updated: April 18, 2025

Mathematics Application of Trigonometry MCQS Online Test

ECAT Math Application of Trigonometry Chapter Online Test

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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ECAT Math Application of Trigonometry Test

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

721325

13078800

12895

1001

2. Circum radius of a circle is denoted by

r₂

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

5000 square units

6000 square units

9000 square units

7000 square units

5. R =

c/2sinϒ

a/2sina

a/2sinϒ

a/2sinβ

6. a/sina = b/sinβ – c/sinϒ is law of

Sine

Cotangent

Cosine

Tangent

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

Angle of elevation

Angle of depression

None of these

Right angle

8. 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)

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

10.5

10. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₃

r₂

r₁

11. Law of cosine is

c²=a²+b² – 2ab Cos y

All of these

Cos a = b²+c²–a²/2bc

a² + 2ab cos a = b² + c²

12. r₃ =

∆/s – b

s – a/∆

∆/s – c

∆/s – a

13. cot a/2 =

14. 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

None of these

15 m

20 m

15. 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

3(1 + √3)m

None of these

6(1 + √3)m

(1 + √3)m

16. 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

30°

60°

45°

17. 1/ab + 1/bc + 1/ca =

2rR

R/2r

r/2R

1/2rR

18. Number of elements of triangle is known as

None of these

Vectors

Trigonometry

Algebra

19. √rr₁r₂r₃ = ?

∆

½ bc sin β

sin a

∆/abc

20. Sum of opposite angles of a cyclic quadrilateral is

360°

270°

120°

180°

21. 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

22. r₃ =

s tan a

s tan ϒ/2

s tan a/2

s tan β/2

23.

24. 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°

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

4860.8

190

4300.85

Page 2 of 2

26. 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 4/9

tan⁻¹ 1/9

tan⁻¹ 5/9

27. In ∆ ABC, a²+b²-c²/2ab is

None of these

Cos β

Cos ϒ

Cos a

28. Which one is true?

a²+b²+c² = 2abcos a

cos a = a²+b²+c²/2ab

a²=b²+c² - 2bc cos a

b² = a²+c²+2ac cos β

29. Hero’s formula is used to calculate

Angles of ∆

None of these

Sides of ∆

Area of ∆

30. 4R cos ½ a sin ½ β cos ½ ϒ =

r₂

r₃

r₁

31. 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

377 m

100 m

477 m

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

None of these

Depression

Elevation

Altitude

33. 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

Right angle

Constant angle

Angle of depression

34. R =

a/2sinβ

c/2sina

b/sinβ

c/2sinϒ

35. Pythagorous theorem is solve

Right – triangles

Rectangles

None of these

Oblique triangles

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

Angle of depression

Constant angle

Angle of elevation

Right angle

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

External bisectors of A and C and internal bisector of B

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

38.

39.

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

a²sina/2sinβ sinϒ

b²sina/2sinβ sinϒ

c²sina/2sinβ sinϒ

a²sinβ sinϒ/2 sin a

41. 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 = 13.3, c = 43.8

B = 113.3, c = 143.8

42. 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

In – center

Circum – Center

Ex – center

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

50°

45°

550°

40°

44.

45. E – radius corresponding to

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Mustansar KhanLast Updated: April 18, 2025

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ECAT Mathematics Application of Trigonometry Online Test

Mathematics Application of Trigonometry MCQS Online Test

ECAT Math Application of Trigonometry Chapter Online Test

ECAT Math Application of Trigonometry Test

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