This is the Multiple Choice Questions Part 1 of the Series in Plane 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 Trigonometry | MCQs in Solution to Right Triangles | MCQs in Pythagorean Theorem | MCQs in Solution to Oblique Triangles | MCQs in Law of Sines | MCQs in Law of Cosines | MCQs in Law of Tangents | MCQs in Trigonometric Identities | MCQs in Plane Areas (Triangles) | MCQs in Plane Areas (Quadrilaterals) | MCQs in Ptolemy’s Theorem

### Online Questions and Answers in Plane Trigonometry Series

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

**Plane Trigonometry MCQs**

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

**PART I**

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

**PART II**

**MCQs from Number 101 – 150**Answer key:

**PART III**

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

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

**Problem 1: ECE Board April 1999**

Sin (B – A) is equal to _______, when B = 270 degrees and A is an acute angle.

- A. – cos A
- B. cos A
- C. – sin A
- D. sin A

**Problem 2: ECE Board April 1999**

If sec^{2 }A is 5/2, the quantity 1 – sin^{2} A is equivalent to?

- A. 2.5
- B. 1.5
- C. 0.4
- D. 0.6

**Problem 3: ECE Board April 1999**

(cos A)^{4} – (sin A)^{4} is equal to ______.

- A. cos 4A
- B. cos 2A
- C. sin 2A
- D. sin 4A

**Problem 4: ECE Board April 1999**

Of what quadrant is A, if sec A is positive and csc A is negative?

- A. IV
- B. II
- C. III
^{} - D. I

**Problem 5: ME Board October 1996**

Angles are measured from the positive horizontal axis, and the positive direction is counter clockwise. What are the values of sin B and cos B in the 4^{th} quadrant?

- A. sin B > 0 and cos B < 0
- B. sin B < 0 and cos B < 0
- C. sin B > 0 and cos B > 0
- D. sin B < 0 and cos B > 0

**Problem 6: ECE Board November 1998**

Csc 520^{o} is equal to

- A. cos 20
^{o} - B. csc 20
^{o} - C. tan 45
^{o} - D. sin 20
^{o}

**Problem 7: ECE Board April 1993**

Solve for Î¸ in the following equation: Sin 2Î¸ = cos Î¸

- A. 30
^{o}^{} - B. 45
^{o} - C. 60
^{o} - D. 15
^{o}

**Problem 8: CE Board November 1993**

If sin 3A = cos 6B, then

- A. A + B = 90
^{o} - B. A + 2B = 30
^{o} - C. A + B = 180
^{o} - D. None of these

**Problem 9: EE Board October 1996**

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

- A. 20.705
^{o} - B. 30.705
^{o} - C. 35.705
^{o} - D. 15.705
^{o}

**Problem 10: EE Board October 1997**

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

- A. 32.2
^{o}, 69.3^{o} - B. – 20.67
^{o}, 69.3^{o} - C. 20.90
^{o}, 69.1^{o} - D. – 32.2, 69.3
^{o}

**Problem 11: EE Board April 1997**

Solve for G is csc (11G – 16 degrees) = sec (5G + 26 degrees).

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

**Problem 12: EE Board April 1992**

Find the value of A between 270^{o} and 360^{o} if sin ^{2} A – sin A = 1.

- A. 300
^{o} - B. 320
^{o} - C. 310
^{o} - D. 330
^{o}^{}

**Problem 13: CE Board November 1993**

If cos 65^{o} + cos 55^{o }= cos Î¸, find the Î¸ in radians.

- A. 0.765
^{} - B. 0.087
- C. 1.213
- D. 1.421

**Problem 14: CE Board November 1992**

Find the value of sin (arc cos 15/17 ).

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

**Problem 15: EE Board October 1991**

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

**Problem 16: EE Board March 1998**

If , determine the angle of A in degrees.

- A. 5
^{o} - B. 6
^{o} - C. 3
^{o} - D. 7
^{o}

**Problem 17: CE Board November 1992**

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

**Problem 18: CE Board November 1993**

Find the value of y in the given: y = (1 + cos 2Î¸) tan Î¸.

- A. sin Î¸
- B. cos Î¸
- C. sin 2Î¸
- D. cos 2Î¸

**Problem 19: CE Board May 1992**

- A. 2 sin Î¸
- B. 2 cos Î¸
- C. 2 tan Î¸
- D. 2 cot Î¸

**Problem 20: ME Board April 1996**

Simplify the equation sin^{2 }Î¸ (1 + cot^{2 }Î¸)

- A. 1
- B. sin
^{2 }Î¸ - C. sin
^{2 }Î¸ sec^{2 }Î¸ - D. sec
^{2 }Î¸

**Problem 21: ME Board October 1995**

Simplify the expression sec Î¸ – (sec Î¸) sin^{2} Î¸

- A. cos
^{2}Î¸ - B. cos Î¸
- C. sin
^{2}Î¸ - D. sin
^{ }Î¸

**Problem 22: ME Board April 1998**

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

**Problem 23: EE Board October 1992**

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

- A. 30
^{o} - B. 45
^{o} - C. 60
^{o} - D. 90
^{o}

**Problem 24: ECE Board March 1996**

Solve for x in the given equation: Arc tan (2x) + arc tan (x) = Ï€/4

- A. 0.149
^{} - B. 0.281
- C. 0.421
- D. 0.316

**Problem 25: EE Board March 1998**

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

- A. 1.5
^{} - B. 1.34
- C. 1.20
- D. 1.25

**Problem 26: ECE Board November 1998**

Solve for A for the given equation cos^{2 }A = 1 – cos^{2 }A.

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

**Problem 27:ECE Board April 1991**

Evaluate the following:

- A. 1
^{} - B. 0
- C. 45.5
- D. 10

**Problem 28: ECE Board April 1991**

Simplify the following:

- A. 0
^{} - B. sin A
- C. 1
- D. cos A

**Problem 29: ECE Board April 1991**

Evaluate:

- A. sin Î¸
^{} - B. cos Î¸
- C. tan Î¸
- D. cot Î¸

**Problem 30: ECE Board April 1994**

Solve for the value of “A” when sin A = 3.5x and cos A = 5.5x.

- A. 32.47°
^{} - B. 33.68°
- C. 34.12°
- D. 35.21°

**Problem 31: ECE Board November 1996**

If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x?

- A. 0.265
^{} - B. 0.256
- C. 0.562
- D. 0.625

**Problem 32: CE Board May 1994**

If coversed sin Î¸ = 0.134, find the value of Î¸.

- A. 30
^{o} - B. 45
^{o} - C. 60
^{o} - D. 90
^{o}

**Problem 33: ME Board April 1991**

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

- A. 39.49
^{} - B. 35.50
- C. 30.74
- D. 42.55

**Problem 34: ECE Board April 1998**

Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32° W of N and from B the bearing of C is 26° 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

**Problem 35: ECE Board November 1998**

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

**Problem 36: GE Board August 1994**

A ship started sailing S 42°35’ W at the rate of 5kph. After 2 hours, ship B started at the same port going N 46°20’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

**Problem 37: ME Board April 1993**

An aerolift airplane can fly at an airspeed of 300 mph. If there is a wind blowing towards the cast at 50mph, what should be the plane’s compass heading in order for its course to be 30°? What will be the plane’s ground speed if it flies in this course?

- A. 19.7, 307.4 mph
^{} - B. 20.1, 309.4 mph
- C. 21.7, 321.8 mph
- D. 22.3, 319.2 mph

**Problem 38: ECE Board April 1998**

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

- A. 76.31 m
^{} - B. 73.31 m
- C. 73.16 m
- D. 73.61 m

**Problem 39: ECE Board April 1994**

A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole is leaned 15° 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

**Problem 40: ME Board November 1994**

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

- A. 24 ft, 53.13°
^{} - B. 24 ft, 36.87°
^{} - C. 24 ft, 53.13°
^{} - D. 25 ft, 36.87°

**Problem 41: CE Board November 1997**

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

- A. 66.3 m
^{} - B. 79.3 m
- C. 87.2 m
- D. 90.7 m

**Problem 42: CE Board November 1997**

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 top of the building from points A and B are 21° and 32° respectively. How far is A from the building in meters.?

- A. 259.28
^{} - B. 265.42
- C. 271.64
- D. 277.29

**Problem 43: ECE Board November 1991**

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

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

**Problem 44: ME Board April 1997**

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 30° and at point B is 40°. What is the height of the tower?

- A. 85.60 feet
^{} - B. 92.54 feet
- C. 110.29 feet
- D. 143.97 feet

**Problem 45: ME Board April 1993**

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 13° and 35° respectively. The height of the tower is 50 m. Find the height of the monument.

- A. 29.13 m
^{} - B. 30.11 m
- C. 32.12 m
- D. 33.51 m

**Problem 46: ECE Board November 1998**

If an equilateral 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

**Problem 47: EE Board October 1997**

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

- A. 197.49 m
^{} - B. 218.61 m
- C. 341.78 m
- D. 282.15 m

**Problem 48: EE Board October 1997**

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

**Problem 49: EE Board October 1997**

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

**Problem 50:ECE Board April 1998**

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

- A. 240
^{} - B. 420
- C. 320
- D. 200

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