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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.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

ECAT Math Application of Trigonometry Test

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1. 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

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. R =

a/2sina

c/2sinϒ

a/2sinϒ

a/2sinβ

4. 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

6(1 + √3)m

None of these

(1 + √3)m

5. cot a/2 =

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

5000 square units

7000 square units

9000 square units

6000 square units

7. r₃ =

∆/s – c

∆/s – a

s – a/∆

∆/s – b

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

Angle of elevation

Constant angle

Angle of depression

Right angle

9. Circum radius of a circle is denoted by

r₂

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

c²sina/2sinβ sinϒ

a²sina/2sinβ sinϒ

b²sina/2sinβ sinϒ

a²sinβ sinϒ/2 sin a

11. 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

100 m

377 m

477 m

225 m

12. In ∆ ABC, a²+b²-c²/2ab is

Cos a

None of these

Cos β

Cos ϒ

13.

14.

15. 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 5/9

tan⁻¹ 2/9

tan⁻¹ 1/9

tan⁻¹ 4/9

16. √rr₁r₂r₃ = ?

∆

½ bc sin β

∆/abc

sin a

17. Which one is true?

cos a = a²+b²+c²/2ab

a²+b²+c² = 2abcos a

b² = a²+c²+2ac cos β

a²=b²+c² - 2bc cos a

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

180°

90°

53°7’

19. Pythagorous theorem is solve

Oblique triangles

None of these

Rectangles

Right – triangles

20. 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 B and C and internal bisectors of A

External bisectors of A, B and C

External bisector of A and B and internal bisector of C

21. 4R cos ½ a sin ½ β cos ½ ϒ =

r₁

r₃

r₂

22. 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)

23.

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

B = 13.3, c = 43.8

B = 113.3, c = 143.8

B = 143.8, c = 113.3

B = 43.8, c = 13.3

25. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₁

r₂

r₃

Page 2 of 2

26. Law of cosine is

c²=a²+b² – 2ab Cos y

All of these

a² + 2ab cos a = b² + c²

Cos a = b²+c²–a²/2bc

27. 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°

30°

None of these

45°

28. Hero’s formula is used to calculate

Area of ∆

None of these

Sides of ∆

Angles of ∆

29. 1/ab + 1/bc + 1/ca =

r/2R

2rR

1/2rR

R/2r

30.

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

Sine

Cosine

Tangent

Cotangent

32. E – radius corresponding to

33. Sum of opposite angles of a cyclic quadrilateral is

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

36. Number of elements of triangle is known as

Trigonometry

None of these

Vectors

Algebra

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

190

4300.85

4860.8

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

13078800

721325

1001

12895

39. 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

Ex – center

In – center

None of these

Circum – Center

40. R =

a/2sinβ

b/sinβ

c/2sinϒ

c/2sina

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

Elevation

Depression

None of these

Altitude

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

10 m

None of these

15 m

20 m

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

10.5

44. 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

Angle of elevation

Constant angle

Right angle

45. r₃ =

s tan a

s tan ϒ/2

s tan a/2

s tan β/2

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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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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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