Topic 3: Trigonometry
1. If the sum of two angles equal to 360 degrees, it is called
A Complementary Angles
C Supplementary Angles
B Explementary Angles
D Adjacent Angles
2. A geometrical figure having identical size and shape.
A Congruent
C Concurrent
B Conjugate
D Similar
3. The point of concurrency of the altitude of a triangle.
A Centroid
C Incenter
B Orthocenter
D Circumcenter
4. An angle greater than 180 degrees but less than 360 degrees.
A Complex
C Reflex
B Obtuse
D Exterior
5. The highest point of figure with respect to the base or the plane of the base.
A Apothem
C Altitude
B Peak
D Apex
6. The case of a solution of a plane triangle where the given data leads to two solutions.
A Quadratic Equation
C Extraneous Solution
B Ambiguous Solution
D None of these
7. An equilateral polygon or sometimes known as regular polygon.
A Equigon
C Perigon
B Isogon
D Decagon
8. The angle that the line of sight to the object makes with the horizontal is above the eye of
the observer.
A Angle of Elevation
C Acute Angle
B Angle of Depression
D Secondary Angle
9. An angle with no equal side is known as
A Scalene Triangle
B Isosceles Triangle
C
D
Oblique Triangle
Equilateral Triangle
10. The most proved theorem in Mathematics.
A Fermat’s Theorem
B Gauss’ Theorem
C
D
Ptolemy’s Theorem
Pythagorean Theorem
11. Express 180 in mils.
A 220 mils
B 320 mils
C
D
400 mils
480 mils
12. If Tan A = 1/3 and Cot B = 4, then Tan (A+B) is equal to
A 11/7
C 7/12
B 7/11
D 12/7
13. Solve for the value of A if Sin2 A + 4 Sin A + 3 = 0.
A 
C /4
B /2
D 3 / 2
14. Simplify the expression Sec A – Sec A Sin2A.
A Sin A
B Cos A
C
D
Csc A
Sec A
trigonometry / page 2
15. Solve for x if Arctan (x+1) + Arctan (x-1) = Arctan (12)
A 1.5
C 1.25
B 1.33
D 1.2
16. Solve for x if Sin 4x = Cos (400 + x).
A 100
B 200
C
D
300
400
17. Solve for x if Tan 3x = 5 Tan x.
A 15.7050
B 20.7050
C
D
30.7050
40.7050
18. Simplify Cos (300 – A) – Cos (300 + A) as a function of A only.
A Cos A
C Tan A
B Sec A
D Sin A
19. Simplify Cos (A + B) Cos A + Sin (A + B) Sin A.
A Sin B
C
B Cos B
D
20. Evaluate the expression:
A 0
B 1
Sin A
Cos A
Ошибка!
C
D
30
45
21. Find the quadrant of A, if Sec A is positive and Csc A is negative?
A Quadrant I
C Quadrant III
B Quadrant II
D Quadrant IV
22. Find the value of x, if Sin 2A = 3.939x, Sin A = 2.511x and Cos A = 3.06x.
A 0.265
C 0.562
B 0.256
D 0.625
23. In triangle ABC, the angle at A is double that at B and the angle at B is double that at C. If A,
B and C are in degrees, find the measure of the angle at C.
A 23.150
C 25.710
B 24.610
D 28.160
24. The interior of the angle of a regular polygon measures 1440. The polygon has _____ sides.
A 12
C 8
B 10
D 6
25. How many diagonals are there in a polygon of 20 sides?
A 200
C 100
B 170
D 158
26. The legs of a right triangle are in the ratio 2:3 and its area is 108 sq. cm. Find the perimeter
of the triangle.
A 21.63 cm
C 41.63 cm
B 31.63 cm
D 51.63 cm
27. A pole cast a shadow 15 m long when the angle of elevation of the sun is 61 0. If the pole has
lean 150 from the vertical directly toward the sun, what is the length of the pole?
A 54.23 m
C 36.84 m
B 48.6 m
D 64.84 m
trigonometry / page 3
28. 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 triangle be?
A 240
C 230
B 320
D 200
29. The area of the isosceles triangle is 36 sq m with the included angle of 30 between the two
equal sides. Find the perimeter of the triangle.
A 30.21 m
C 28.34 m
B 32.12 m
D 29.65 m
30. If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side
of the triangle.
A 66.44 cm
C 34.64 cm
B 63.44 cm
D 36.46 cm
31. A PLDT tower and a monument stand on a level ground. The angles of depression of the top
and bottom of the monument viewed from the top of the PLDT tower are 130 and 350
respectively. The height of the tower is 50 m. Find the height of the monument.
A 29.13 m
C 33.51 m
B 30.11 m
D 32.12 m
32. From the top and bottom of a 74 – ft lighthouse, the angle of depression of a ship are 410
and 370 respectively. Find the height of the lighthouse above sea level.
A 625.8 ft
C 755.8 ft
B 725.8 ft
D 555.8 ft
33. At one side of the road is a 25 ft pole fixed on top of a 15 ft wall. On the other side of the
road, the flagstaff and the wall subtend equal angle. Find the width of the road.
A 40 ft
C 25 ft
B 55 ft
D 30 ft
34. Find the radius of circle circumscribed about the triangle for which A = 500, B = 200 , and
a = 35 inches.
A 25.64 in
C 22.84 in
B 31.25 in
D 36.55 in
35. What is the radius of the circle, if a central angle of 1100 subtends a chord of length 84
inches?
A 34.4 in
C 48.4 in
B 68.8 in
D 51.1 in
36. A television antenna stands on the edge of the top of a 52 – story building. From a point 320
ft. from the base of the building, the angle of elevation of the top of the antenna is 64 0. If
each story of the building is 12 ft high, find the height of the antenna.
A 35.3 ft
C 31.2 ft
B 33.5 ft
D 32.1 ft
37. A circle is divided into two parts by a chord 3 cm away from the center. Find the area of the
smaller part if the circle has an area of 201 cm2.
A 57.3 cm2
C 53.7 cm2
2
B 37.5 cm
D 35.7 cm2
38. Find the length of the common chord of two circles of radii 25 cm and 26 cm, respectively, if
the distance between their centers is 17 cm.
A 36 cm
C 48 cm
B 40 cm
D 54 cm
trigonometry / page 4
39. Two towers A and B are placed at a distance of 100 m apart horizontally. The height of A is
40 m and that of B is 30 m. At what distance vertically above the ground will the intersection
of the lines forming the angles of elevation of the two towers are observed from the bases of
towers A and B respectively.
A 57.14 m
C 17.143 m
B 42.86 m
D 18.193 m
40. The bearing of B from A is 700 North of East; the bearing of C from B is 600 South of East
and the bearing of A from C is 200 South of West. If AB is 10 meters, find the length of BC.
A 4.8 m
C 6.8 m
B 5.8 m
D 7.8 m