ECAT Mathematics Application of Trigonometry Online Test

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

2. 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

3. 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).

4. r₃ =

5. Pythagorous theorem is solve

6. In ∆ ABC, a²+b²-c²/2ab is

8. Number of elements of triangle is known as

10. 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

11. 1/ab + 1/bc + 1/ca =

12. 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

13. 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

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

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

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

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

18. R =

19. 4R cos ½ a sin ½ β cos ½ ϒ =

20. 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

22. 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 =

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

24. E – radius corresponding to

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

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

31. 4 R sin a/2 sin β/2 sin ϒ/2 =

32. Law of cosine is

33. R =

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

36. cot a/2 =

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

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

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

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

41. Sum of opposite angles of a cyclic quadrilateral is

42. r₃ =

43. Which one is true?

44. Hero’s formula is used to calculate

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