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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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Page 1 of 2

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

c²sina/2sinβ sinϒ

b²sina/2sinβ sinϒ

a²sinβ sinϒ/2 sin a

a²sina/2sinβ sinϒ

2. In ∆ ABC, a²+b²-c²/2ab is

Cos β

Cos ϒ

None of these

Cos a

3. R =

c/2sina

b/sinβ

c/2sinϒ

a/2sinβ

4. Law of cosine is

All of these

a² + 2ab cos a = b² + c²

c²=a²+b² – 2ab Cos y

Cos a = b²+c²–a²/2bc

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

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, B and C

External bisectors of A and C and internal bisector of B

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

Depression

Altitude

Elevation

None of these

7. 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).

150(√3+1)

100/√3

100√3

9. 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°

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

a+b+c

a+b+c/4

a+b+c/3

a+b+c/2

11. r₃ =

s tan a/2

s tan ϒ/2

s tan β/2

s tan a

12. 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

477 m

100 m

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

4860.8

4300.85

190

14. 1/ab + 1/bc + 1/ca =

r/2R

2rR

R/2r

1/2rR

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

Angle of elevation

Constant angle

16. cot a/2 =

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

6000 square units

5000 square units

9000 square units

7000 square units

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

B = 13.3, c = 43.8

B = 143.8, c = 113.3

B = 43.8, c = 13.3

B = 113.3, c = 143.8

19. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₁

r₂

r₃

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

1001

721325

13078800

12895

21. 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

In – center

Ex – center

22. Sum of opposite angles of a cyclic quadrilateral is

180°

360°

120°

270°

23. Circum radius of a circle is denoted by

r₂

24.

25.

Page 2 of 2

26. R =

a/2sinϒ

c/2sinϒ

a/2sinβ

a/2sina

27.

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

10.5

29. Number of elements of triangle is known as

Algebra

Vectors

Trigonometry

None of these

30. r₃ =

∆/s – b

∆/s – a

s – a/∆

∆/s – c

31. 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

32. E – radius corresponding to

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

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

Angle of depression

Right angle

Constant angle

Angle of elevation

36. 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

37. Which one is true?

b² = a²+c²+2ac cos β

a²=b²+c² - 2bc cos a

a²+b²+c² = 2abcos a

cos a = a²+b²+c²/2ab

38. 4R cos ½ a sin ½ β cos ½ ϒ =

r₃

r₂

r₁

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

None of these

Angle of depression

Right angle

Angle of elevation

40. Hero’s formula is used to calculate

Sides of ∆

Area of ∆

None of these

Angles of ∆

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

180°

53°7’

90°

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

Tangent

Cosine

Sine

Cotangent

43. Pythagorous theorem is solve

Rectangles

Oblique triangles

None of these

Right – triangles

44. 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 5/9

tan⁻¹ 1/9

tan⁻¹ 2/9

45. √rr₁r₂r₃ = ?

∆/abc

∆

sin a

½ bc sin β

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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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