This is the Multiple Choice Questions Part 1 of the Series in Trigonometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

### Multiple Choice Questions Topic Outline

- MCQs in Logarithmic Principles | MCQs in Trigonometric Functions | MCQs in Fundamental Trigonometric Identities | MCQs in Solution of Right and Oblique Triangles | MCQs in Applications of Terrestrial Mensuration | MCQs in Area, Perimeter and Centroid of Plane Figures | MCQs in Polar Coordinates | MCQs in Spherical Trigonometry

### Start Practice Exam Test Questions Part I of the Series

**Choose the letter of the best answer in each questions.**

1. Csc 520ยฐ is equal to:

- A. cos 20ยฐ
- B. csc 20ยฐ
- C. tan 45ยฐ
- D. sin 20ยฐ

2. Solve for the ฮธ in the following equation: Sin 2ฮธ = cos ฮธ

- A. 30ยฐ
- B. 45ยฐ
- C. 60ยฐ
- D. 15ยฐ

3. If sin 3A = cos 6B, the

- A. A + B = 0ยฐ
- B. A + 2B = 30ยฐ
- C. A + B = 180ยฐ
- D. None of these

4. Solve for x, if tan 3x = 5 tan x

- A. 20.705ยฐ
- B. 30.705ยฐ
- C. 35.705ยฐ
- D. 15.705ยฐ

5. If sin x cos x + sin 2x = 1, what are the values of x?

- A. 32.2ยฐ, 69.3ยฐ
- B. -20.67ยฐ, 69.3ยฐ
- C. 20.90ยฐ, 69.1ยฐ
- D. -32.2ยฐ, 69.3ยฐ

6. Solve for G if csc (11G โ 16 degrees) = sec (5G + 26 degrees)

- A. 7 degrees
- B. 5 degrees
- C. 6 degrees
- D. 4 degrees

7. Find the value of A between 270o and 360o if sin^2 A โ sin A = 1

- A. 300ยฐ
- B. 320ยฐ
- C. 310ยฐ
- D. 330ยฐ

8. If cos 65ยฐ + cos 55ยฐ = cos ฮธ, find ฮธ in radians

- A. 0.765
- B. 0.087
- C. 1.213
- D. 1.421

9. Find the value of sin (arc cos15/17)

- A. 8/11
- B. 8/19
- C. 8/15
- D. 8/17

10. The sine of a certain angle is 0.6, calculate the cotangent of the angle.

- A. 4/3
- B. 5/4
- C. 4/5
- D. 3/4

11. If sec 2A =1/sin13A, determine the angle A in degrees.

- A. 5ยฐ
- B. 6ยฐ
- C. 3ยฐ
- D. 7ยฐ

12. If tan x =1/2, tan y = 1/3, what is the value of tan (x + y)?

- A. 1/2
- B. 1/6
- C. 2
- D. 1

13. Find the value of y in the given: y = (1 + cos ฮธ) tan ฮธ

- A. sin ฮธ
- B. cos ฮธ
- C. sin 2ฮธ
- D. cos 2ฮธ

14. Find the value of (sin ฮธ + cos ฮธ tanฮธ)/cos ฮธ

- A. 2 sin ฮธ
- B. 2 cos ฮธ
- C. 2 tan ฮธ
- D. 2 cot ฮธ

15. Simplify the equation sin^2ฮธ(1 + cot^2ฮธ)

- A. 1
- B. sin^2ฮธ
- C. sin^2ฮธsec^2ฮธ
- D. sec^2ฮธ

16. Simplify the expression sec ฮธ โ (sec ฮธ)sin^2ฮธ

- A. cos^2ฮธ
- B. cos ฮธ
- C. sin^2ฮธ
- D. sin ฮธ

17. Arc tan [2 cos (arc sin [(3^(1/2))/2]) / 2]) is equal to

- A. ฯ/3
- B. ฯ/4
- C. ฯ/16
- D. ฯ/2

18. Evaluate arc cot [2cos (arc sin 0.5)]

- A. 30ยฐ
- B. 45ยฐ
- C. 60ยฐ
- D. 90ยฐ

19. Solve for x in the given equation: Arc tan (2x) + arc tan (x) = ฯ/4

- A. 0.149
- B. 0.281
- C. 0.421
- D. 0.316

20. Solve for x in the equation: arc tan (x + 1) + arc tan (x โ 1) = arc tan (12)

- A. 1.5
- B. 1.34
- C. 1.20
- D. 1.25

21. Solve for A for the given equation cos 2A = 1 โ cos 2A

- A. 45, 125, 225, 335 degrees
- B. 45, 125, 225, 315 degrees
- C. 45, 135, 225, 315 degrees
- D. 45, 150, 220, 315 degrees

22. Evaluate the following:

- A. 1
- B. 0
- C. 45.5
- D. 10

23. Simplify the following:

[(cos A + cos B)/(sin A โ sin B)] + [(sin A + sin B)/(cos A โ cos B)]

- A. 0
- B. sin A
- C. 1
- D. cos A

24. Evaluate: (2sinฮธcosฮธ-cosฮธ)/(1 โ sin ฮธ+ sin^2ฮธ โ cos^2ฮธ)

- A. sin ฮธ
- B. cos ฮธ
- C. tan ฮธ
- D. cot ฮธ

25. Solve for the value of Aยฐ when sin A = 3.5 x and cos A = 5.5 x

- A. 32.47ยฐ
- B. 33.68ยฐ
- C. 34.12ยฐ
- D. 3521ยฐ

26. If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.39x, find the value of x?

- A. 0.265
- B. 0.256
- C. 0.562
- D. 0.625

27. If conversed sin ฮธ= 0.134, find the value of ฮธ

- A. 30ยฐ
- B. 45ยฐ
- C. 60ยฐ
- D. 90ยฐ

28. A man standing on a 48.5 meter building high, has an eyesight height of 1.5m from the top of the building, took a depression reading from the top of another nearby building and nearest wall, which are 50ยฐ and 80ยฐ respectively. Find the height of the nearby building in meters. The man is standing at the edge of the building lie on the same horizontal plane.

- A. 39.49
- B. 35.50
- C. 35.50
- D. 42.55

29. Points A and B 1000m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32ยฐ W of N and from B the bearing of C is 26ยฐ N of E. Approximate the shortest distance of tower C to the highway.

- A. 364 m
- B. 374 m
- C. 384 m
- D. 394 m

30. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes, if the areas of the triangles differ by 21 square units.

- A. 6 and 12
- B. 3 and 9
- C. 5 and 11
- D. 4 and 10

31. A ship started sailing S 42ยฐ35โ W at the rate of 5 kph. After 2 hours, ship B started at the same port going N 46o20โ W at the rate of 7 kph. After how many hours will the second ship be exactly north of ship A?

- A. 3.68
- B. 4.03
- C. 5.12
- D. 4.83

32. An aero lift airplane can fly at airspeed of 300 mph. If there is a wind blowing towards the cast at 50 mph, what should be the planeโs compass heading in order for its course to be 30o? What will be the planeโs ground speed if it flies in the course?

- A. 19.7ยฐ, 307.4 mph
- B. 20.1ยฐ, 309. mph
- C. 21.7ยฐ, 321.8 mph
- D. 22.3ยฐ, 319.2 mph

33. A man finds the angle of elevation of the top of a tower to be 30o. He walks 85m nearer the tower and finds its angle of elevation to be 60o. What is the height of the tower?

- A. 76.31m
- B. 73.31m
- C. 73.16m
- D. 73.61m

34. A pole cast a shadow 15 m long when the angle of elevation of the sun is 61ยฐ. If the pole is leaned 15ยฐ from the vertical directly towards the sun, determine the length of the pole.

- A. 54.23 m
- B. 48.23 m
- C. 42.44 m
- D. 46.21 m

35. A wire supporting a pole is fastened to it 20 feet from the ground and to the ground 15 feet from the pole. Determine the length of the wire and the angle it makes with the pole.

- A. 24 ft, 53.13ยฐ
- B. 24 ft, 36.87ยฐ
- C. 25 ft, 53.13ยฐ
- D. 25 ft, 36.87ยฐ

36. The angle of elevation of the top of the tower B from the top of tower A is 28ยฐ and the angle of elevation of the top of the tower A from the base of tower B is 46ยฐ. The two towers lie in the same horizontal plane. If the height of the tower B is 120m, find the height of tower A.

- A. 66.3m
- B. 79.3m
- C. 87.2m
- D. 90.7m

37. Points A and B are 100 m apart and are of the same elevation as the foot of a building. The angles of elevation of the building from the points A and B areยฐ and 32ยฐ respectively. How far is A from the building in meters?

- A. 259.28
- B. 265.42
- C. 271.64
- D. 277.29

38. The captain of a ship views the top of a lighthouse at an angle ofยฐ 60ยฐ with the horizontal at an elevation of 6 meters above the sea level. Five minutes later, the same captain of the ship views the top of the same lighthouse at an angle of 30ยฐ with the horizontal. Determine the speed of the ship if the lighthouse is known to be 50 meters above the sea level.

- A. 0.265 m/sec
- B. 0.155 m/sec
- C. 0.169 m/sec
- D. 0.210 m/sec

39. An observer wishes to determine the height of a tower. He takes sights at the top of the tower from A and B, which are 50 feet apart, at the same elevation on a direct line with the tower. The vertical angle at point A is 30ยฐ and at point B is 40ยฐ. What is the height of the tower?

- A. 85.60 feet
- B. 92.54 feet
- C. 110.29 feet
- D. 143.97 feet

40. A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower at 13ยฐ and 35ยฐ respectively. The height of the tower is 50m. Find the height of the monument.

- A. 29.13 m
- B. 30.11 m
- C. 32.12 m
- D. 33.51 m

41. If an equivalent triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle.

- A. 34.64 cm
- B. 64.12 cm
- C. 36.44 cm
- D. 32.10 cm

42. The two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150m side is 26ยฐ. What is the third side?

- A. 197.49 m
- B. 218.61 m
- C. 341.78 m
- D. 282.15 m

43. The sides of a triangular lot are 130 m, 180 m and 190 m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line.

- A. 120 m
- B. 130 m
- C. 125 m
- D. 128 m

44. The sides of a triangle are 195, 157 and 210, respectively. What is the area of the triangle?

- A. 73,250 sq. units
- B. 10,250 sq. units
- C. 14,586 sq. units
- D. 11,260 sq. units

45. The sides of a triangle are 8, 15, and 17 units. If each side is doubled, how many square units will the are of the new triangle be?

- A. 240
- B. 420
- C. 320
- D. 200

46. If Greenwich Mean Time (GMT) is 6 A.M, what is the time at a place located 30ยฐ East longitude?

- A. 7 A.M.
- B. 8 A.M.
- C. 9 A.M.
- D. 4 A.M.

47. If the longitude of Tokyo is 139ยฐE and that of Manila is 121ยฐE, what is the time difference between Tokyo and Manila?

- A. 1 hour and 12 minutes
- B. 1 hour and 5 minutes
- C. 1 hour and 8 minutes
- D. 1 hour and 10 minutes

48. One degree on the equator of the earth is equivalent to _____ in time.

- A. 1 minute
- B. 4 minutes
- C. 30 minutes
- D. 1 hour

49. A spherical triangle ABC has an angle C = 90ยฐ and sides a = 50ยฐ and c = 80ยฐ. Find the value of b in degrees.

- A. 73.22
- B. 74.33
- C. 75.44
- D. 76.55

50. Solve the remaining side of the spherical triangle whose given parts are A = B = 80ยฐ and a = b = 89ยฐ.

- A. 158ยฐ12โ
- B. 162ยฐ21โ
- C. 168ยฐ31โ
- D. 172ยฐ12โ

### Online Questions and Answers in Trigonometry Series

Following is the list of multiple choice questions in this brand new series:

**Trigonometry MCQs**

**MCQs from Number 1 โ 50**Answer key:

**PART I**

**MCQs from Number 51 โ 100**Answer key:

**PART II**

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