ECAT Mathematics Application of Trigonometry Online Test

1. 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

2. Hero’s formula is used to calculate

3. 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

4. Pythagorous theorem is solve

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

7. In ∆ ABC, a²+b²-c²/2ab is

8. Sum of opposite angles of a cyclic quadrilateral is

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

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

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

12. 1/ab + 1/bc + 1/ca =

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

14. R =

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

16. 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

17. 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

18. Law of cosine is

19. Circum radius of a circle is denoted by

20. R =

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

22. Which one is true?

23. r₃ =

25. cot a/2 =

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

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

28. 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 =

29. E – radius corresponding to

36. Number of elements of triangle is known as

37. 4R cos ½ a sin ½ β cos ½ ϒ =

38. 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).

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

41. 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

42. 4 R sin a/2 sin β/2 sin ϒ/2 =

43. r₃ =

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