MCQ in Plane Trigonometry Part 3 | ECE Board Exam Practice

Multiple Choice Questions in Plane Trigonometry – Part 3 | ECE Board Exam Practice

Part 3 already. If you’ve been following this series from the start, your trigonometry foundation is getting stronger with every set you finish.

This part continues the Plane Trigonometry MCQ Series, one of the core topics you’ll face in the Engineering Mathematics section of the ECE Board Exam. The questions compiled here come from past board exam problems, engineering mathematics textbooks, academic journals, and other solid references that ECE reviewees have relied on for years.

By this point in your review, you should be moving past just recognizing formulas. Start connecting the concepts. Notice the patterns in how questions are framed. That’s where real exam readiness begins and not just knowing the formula, but knowing when and how to use it under pressure.

Take your time with each item. If you get something wrong, don’t skip it, that’s actually the most valuable question in the set.

Parts 1 and 2 are still up if you need to go back and fill in any gaps. Otherwise, keep the momentum going and work through every problem here with full focus.

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

Continue Practice Exam Test Questions Part 3 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 10 m, 10 m, and 18 m. 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°. The height of the mountain in feet is:

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 120 m, 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 point 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 40 m x 30 m 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 1.4 m, 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 0.9 m long. What would be the area of the shadow on the ground when the sun is vertically overhead?

A. 0.5 m² 

B. 0.75 m² 

C. 0.84 m² 

D. 0.95 m² 

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°

134. Two straight roads intersect to form an angle of 75 degrees. Find the shortest distance from one road to a gas station on the other road 1 km. from the junction.

A. 2.415 km

B. 4.123 km

C. 3.732 km

D. 5.196 km

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

A. 3.92 cm

B. 5.21 cm

C. 4.73 cm

D. 4.35 cm

136. A television antenna 20 m high stands on top of a house which is 12 m high. At what distance from the base of the house will the antenna and the house subtend equal angle?

A. 24 m

B. 30 m

C. 18 m

D. 20 m

137. An observer 5 meters away from the base of a building finds that the angle of elevation of the top of the building is twice the angle of elevation of the top of the same building when he is 25 m away from it. Find the height of the building.

A. 18.52 m

B. 20.15 m

C. 19.36 m

D. 22.13 m

138. From an airplane flying at 100 m above the ground, the angle of depression of a tower directly to the right of it is 30°. An observer on the base of another tower directly to the left of the airplane finds that the angle of elevation of the airplane is 60°. How far apart are the two towers?

A. 245.21 meters

B. 230.94 meters

C. 216.55 meters

D. 207.85 meters

139. A pole tilts toward the sun at an angle 10° from the vertical casts a shadow 9 meters long. If the angle of elevation from the tip of the shadow to the top of the pole is 43°, how tall is the pole?

A. 9.5 m

B. 11.5 m

C. 10.2 m

D. 8.8 m

140. From a helicopter flying at 30,000 feet, the angles of depression of two towns are 28° and 55°. How far apart are the two towns?

A. 5.92 miles

B. 7.35 miles

C. 8.14 miles

D. 6.71 miles

141. A wall is 15 ft. high and 10 ft. from a building. Find the length of the shortest ladder which will just touch the top of the wall and reach a window 20.5 ft. above the ground.

A. 42.15 feet

B. 48.92 feet

C. 45.54 feet

D. 50.21 feet

142. A ladder, with its foot in the street, makes an angle of 30° with the street when its top rests on a building on one side of the street and makes an angle of 40° with the street when its top rests on a building on the other side of the street. If the ladder is 50 ft. long, how wide is the street?

A. 81.6 feet wide

B. 90.5 feet wide

C. 75.2 feet wide

D. 68.4 feet wide

143. From a point on a level ground, the angles of elevation of the top and bottom of a PLDT tower situated on the top of the hill are measured as 48° and 40°, respectively. Find the height of the hill if the height of tower is 116 feet.

A. 342.15 feet

B. 358.49 feet

C. 325.92 feet

D. 368.21 feet

144. A surveyor wishes to find the width of a river. He set up his transit at C on one bank and sighted across to point A on the opposite bank, then turning through an angle of 90°, he walks 225 m from C to a point B and finally, setting his transit at B, he measured angle BCA as 48.33°. What is the width of the river?

A. 240.5 meters

B. 265.1 meters

C. 230.2 meters

D. 252.8 meters

145. From an airplane flying at 100 m above the ground, the angle of depression of a tower directly to the right of it is 30°. An observer on the base of another tower directly to the left of the airplane finds that the angle of elevation of the airplane is 60°. How far apart are the two towers?

A. 220.85 m

B. 245.21 m

C. 230.94 m

D. 210.55 m

146. Considering the earth as a sphere of radius 6400 km, find the radius of the 60th parallel of latitude.

A. 3,200 km

B. 3,500 km

C. 2,850 km

D. 2,950 km

147. Two towers are 60 m apart. From the top of the shorter tower, the angle of elevation of the top of the taller tower is 40°. How high is the taller tower if the height of the smaller tower is 40 m.

A. 85.12 m

B. 90.35 m

C. 95.21 m

D. 80.55 m

148. The angle of elevation of the top of a light house from a boat 50 m is the compliment of the angle of elevation of the same light house, when the boat is 110 m from it. Find the height of the light house.

A. 70.25 m

B. 78.52 m

C. 68.15 m

D. 74.16 m

149. If the complement of an angle theta is 2/5 of its supplement, then theta is __________.

A. 45°

B. 20°

C. 30°

D. 35°

150. Find the height of a lamp post if the angle of elevation of its top changes from 20 degrees to 40 degrees as the observer 1.8 meters tall advances 23 meters toward the base.

A. 15.68

B. 18.65

C. 16.58

D. 19.48

Online Questions and Answers in Plane Trigonometry Series

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

Online Questions and Answers in Spherical Trigonometry

Mathematics Board Examination Mastery | Math Engineering Pre-Board