This is the Multiple Choice Questions Part 3 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**

### Continue Practice Exam Test Questions Part III of the Series

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

101. The hypotenuse of a right triangle is 34 cm. Find the length of the shortest leg if it is 14 cm shorter than the other leg.

- A. 15 cm
- B. 16 cm
- C. 17 cm
- D. 18 cm

102. A truck travels from point M northward for 30 min. then eastward for one hour, then shifted N 30° W. if the constant speed is 40 Kph, how far directly from M, in km. will be it after 2 hours?

- A. 43.5
- B. 45.2
- C. 47.9
- D. 41.6

103. Two sides of a triangle measures 6 cm. and 8 cm. and their included angle is 40°. Find the third side.

- A. 5.144 cm
- B. 5.263 cm
- C. 4.256 cm
- D. 5.645 cm

104. Given a triangle: C = 100°, a = 15, b = 20. Find c:

- A. 34
- B. 27
- C. 43
- D. 35

105. Given angle A = 32°, angle B = 70°, and side c = 27 units. Solve for side a of the triangle.

- A. 24 units
- B. 10 units
- C. 14.63 units
- D. 12 units

106. In a triangle, find the side c if the angle C = 100°, side b = 20, and side a = 15.

- A. 28
- B. 27
- C. 29
- D. 26

107. Two sides of a triangle are 50 m. and 60 m. long. The angle included between these sides is 30 degrees. What is the interior angle (in degrees) opposite the longest side?

- A. 92.74
- B. 93.74
- C. 94.74
- D. 91.74

108. The sides of a triangle ABC are AB = 15 cm, BC = 18 cm, and CA = 24 cm. Determine the distance from the point of intersection of the angular bisectors to side AB.

- A. 5.21 cm
- B. 3.78 cm
- C. 4.73 cm
- D. 6.25 cm

109. If AB = 15 m, BC = 18 m and CA = 24 m, find the point of intersection of the angular bisector from the vertex C.

- A. 11.3
- B. 12.1
- C. 13.4
- D. 14.3

110. In triangle ABC, angle C = 70 degrees; angle A = 45 degrees; AB = 40 m. what is the length of the median drawn from vertex A to side BC?

- A. 36.8 meters
- B. 37.1 meters
- C. 36.3 meters
- D. 37.4 meters

111. The area of the triangle whose angles are 61°9’32”, 34°14’46”, and 84°35’42” is 680.60. the length of the longest side is:

- A. 35.53
- B. 54.32
- C. 52.43
- D. 62.54

112. Given a triangle ABC whose angles are A = 40°, B = 95° and side b = 30 cm. find the length of the bisector of angle C.

- A. 21.74 cm
- B. 22.35 cm
- C. 20.45 cm
- D. 20.98 cm

113. 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. The length of this dividing line is:

- A. 100 meters
- B. 130 meters
- C. 125 meters
- D. 115 meters

114. From a point outside of an equilateral triangle, the distances to the vertices are 10m, 10m, and 18m. Find the dimension of the triangle.

- A. 25.63
- B. 45.68
- C. 19.94
- D. 12.25

115. 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 degrees N of W and from B the bearing of C is 26 degrees N of E. Approximate the shortest distance of tower C to the highway.

- A. 264 meters
- B. 274 meters
- C. 284 meters
- D. 294 meters

116. An airplane leaves an aircraft carrier and flies South at 350 mph. The carrier travels S 30° E at 25 mph. If the wireless communication range of the airplane is 700 miles, when will it lose contact with the carrier?

- A. after 4.36 hours
- B. after 5.57 hours
- C. after 2.13 hours
- D. after 4.54 hours

117. A statue 2 meters high stands on a column that is 3 meters high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue?

- A. 5√2 meters
- B. 2√5 meters
*C.**20 meters*- D. √10 meters

118. From the top of a building 100 m high, the angle of depression of a point A due East of it is 30°. From a point B due South of the building, the angle of elevation of the top is 60°. Find the distance AB.

- A. 100 + 3√30
- B. 200 – √30
- C. 100 (√30) / 3
- D. 100√3/ 30

119. An observer found the angle of elevation of the top of the tree to be 27°. After moving 10m closer (on the same vertical and horizontal plane as the tree), the angle of elevation becomes 54°. Find the height of the tree.

- A. 8.65 meters
- B. 7.53 meters
- C. 7.02 meters
- D. 8.09 meters

120. From a point A at the foot of the mountain, the angle of elevation of the top B is 60°. After ascending the mountain one (1) mile to an inclination of 30° to the horizon, and reaching a point C, an observer finds that the angle ACB is 135°.

- A. 14386
- B. 12493
- C. 11672
- D. 11223

121. A vertical pole is 10 m from a building. When the angle of elevation of the sum is 45°, the pole cast a shadow on the building 1 m high. Find the height of the pole.

- A. 0 meter
- B. 11 meters
- C. 12 meters
- D. 13 meters

122. A pole cast a shadow of 15 meters long when the angle of elevation of the sun is 61°. If the pole has leaned 15° from the vertical directly toward the sun, what is the length of the pole?

- A. 52.43 meters
- B. 54.23 meters
- C. 53.25 meters
- D. 53.24 meters

123. 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 ft. 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. 85.6 feet
- B. 143.97 feet
- C. 110.29 feet
- D. 92.54 feet

124. From the top of tower A, the angle of elevation of the top of the tower B is 46°. From the foot of tower B the angle of elevation of the top of tower A is 28°. Both towers are on a level ground. If the height of tower B is 120m, how high is tower A in m?

- A. 38.6
- B. 42.3
- C. 44.1
- D. 40.7

125. Points A and B are 100 m apart and are on 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 m?

- A. 271.6
- B. 265.4
- C. 259.2
- D. 277.9

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

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

127. The angle of elevation of a point C from a pint B is 29°42’; the angle of elevation of C from another point A 31.2 m directly below B is 59°23’. How high is C from the horizontal line through A?

- A. 47.1 meters
- B. 52.3 meters
- C. 35.1 meters
- D. 66.9 meters

128. A rectangular piece of land 40m x 30m is to be crossed diagonally by a 10-m wide roadway. If the land cost P1,500.00 per square meter, the cost of the roadway is:

- A. P401.10
- B. P60,165.00
- C. P601,650.00
- D. 651,500.00

129. A man improvises a temporary shield from the sun using a triangular piece of wood with dimensions of 1.4m, 1.5 m, and 1.3 m. with the longer side lying horizontally on the ground, he props up the other corner of the triangle with a vertical pole 0.9m long. What would be the area of the shadow on the ground when the sun is vertically overhead?

- A. 0.5 m
^{2} - B. 0.75 m
^{2} - C. 0.84 m
^{2} - D. 0.95 m
^{2}

130. A rectangular piece of wood 4 cm x 12 cm tall is titled at an angle of 45°. Find the vertical distance between the lower corner and the upper corner.

- A. 4√2 cm
- B. 2√2 cm
- C. 8√2 cm
- D. 6√2 cm

131. A clock has a dial face 12 inches in radius. The minute hand is 9 inches long while the hour hand is 6 inches long. The plane of rotation of the minute hand is 2 inches above the plane of rotation of the hour hand. Find the distance between the tips of the hands at 5:40 AM.

- A. 9.17 inches
- B. 8.23 inches
- C. 10.65 inches
- D. 11.25 inches

132. If the bearing of A from B is 40° W, then the bearing of B from A is:

- A. N 40° E
- B. N 40° W
- C. N 50° E
- D. N 50° W

133. A plane hillside is inclined at an angle of 28° with the horizontal. A man wearing skis can climb this hillside by following a straight path inclined at an angle of 12° to the horizontal, but one without skis must follow a path inclined at an angle of only 5° with the horizontal. Find the angle between the directions of the two paths.

- A. 13.21°
- B. 18.74°
- C. 15.56°
- D. 17.22°

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