SAMAR COLLEGES, Inc.

Catbalogan City
JUNIOR HIGH SCHOOL DEPARTMENT

FOURTH QUARTERLY TEST IN MATHEMATICS 9

NAME: _______________________________ GRADE AND SECTION:

MULTIPLE CHOICE
Direction: Choose the letter of the correct answer on each question.
1. It is a branch of mathematics that studies relationships between side lengths and angles of
triangles.
a. Functions
b. Trigonometric functions
c. Trigonometric ratios
d. Trigonometry
2. It is a function of an angle, or of an abstract quantity, used in trigonometry, including the
sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.
a. Right triangle
b. Trigonometric functions
c. Trigonometric ratios
d. Special Angles
3. It the longest side of a right triangle, opposite the right angle.
a. Adjacent c. Opposite
b. Hypotenuse d. Leg
4. It is the ratio of the side adjacent to a particular acute angle to the side opposite the angle.
a. Tangent c. Secant
b. Cotangent d. Cosine
5. It is the ratio of the hypotenuse to the shorter side adjacent to an acute angle; the
reciprocal of a cosine.
a. Tangent c. Secant
b. Cotangent d. Cosine
6. It is the ratio of the hypotenuse to the side opposite an acute angle; the reciprocal of sine.
a. Cosecant c. Cosine
b. Tangent d. Cotangent
7. It is the trigonometric function that is equal to the ratio of the side adjacent to an acute
angle to the hypotenuse.
a. Secant c. Tangent
b. Cosine d. Cosine
8. What is the reciprocal of sine?
a. Cosecant c. Cosine
b. Tangent d. Cotangent
9. A straight line or plane that touches a curve or curved surface at a point, but if extended
does not cross it at that point.
a. Cosine c. Sine
b. Cotangent d. Tangent

10. It is the trigonometric function that is equal to the ratio of the side opposite a given angle
(in a right triangle) to the hypotenuse.
 a. Sine c. Cosecant
b. Cotangent d. Tangent
11. What is the reciprocal of a cosine?
a. Tangent c. Secant
b. Cotangent d. Cosine
12. What is the value of cos 30°?
a. 0.87 c. 0.89
b. 0.88 d. 0.85
13. What is the value of sin 60°?
a. 0.87 c. 0.89
b. 0.88 d. 0.85
14. What is the value of tan 45°?
a. 4 c. 2
b. 3 d. 1
15. What is the value of sec 45°?
a. 1. 41 c. 1.43
b. 1.42 d. 1.44
16. What is the value of csc 60°?
a. 1.15 c. 1.17
b. 1.16 d. 1.18
17. Line segment AB has a length of 15 and m∠A = 35°. A segment with a length of 12 will
form the third side of the triangle. What are the possible measures of the angle opposite
side AB?
a. 135° c. 136°
b. 134° d. 137°
18. Find cot 60°.
a. 0.58 c. 0.60
b. 0.59 d. 0.61
19. What is csc 80°?
a. 1.0154 c. 1.0156
b. 1.0155 d. 1.0157
20. The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on
a cliff 25 feet above the water makes a 25° angle with the water. To the nearest foot,
how far is the boat from the cliff?

a. 141 ft c. 27f ft
b. 128 ft d. 75 ft

21. An angle between the horizontal plane and line of sight from the observer's eye to some
object above.
a. Angle of depression
b. Angle of elevation
c. Angle of Inclination
 d. Line of sight
22. The line which is drawn from the eyes of the observer to the point being viewed on the
object is known as the ___________.
a. Angle of depression
b. Angle of elevation
c. Angle of Inclination
d. Line of sight
23. The angle formed by the line of sight and the horizontal plane for an object below the
horizontal.
a. Angle of depression
b. Angle of elevation
c. Angle of Inclination
d. Angle of depression and elevation
24. A 109 ft tree casts a shadow that is 130 ft long. What is the angle of elevation of the sun?
a. 50° c. 40°
b. -50° d. -40°
25. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole
and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to
be 44°. To the nearest foot, what is the height of the pole?
a. 145 ft c. 135 ft
b. 149 ft d. 139 ft
26. An airplane pilot over the Pacific sights an atoll at an angle of depression of 5°. At this
time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the
height of the plane to the nearest meter?
a. 403 m c. 4611 m
b. 405 m d. 4647 m
27. Triangle ABC has side lengths 9, 40, and 41. Do the side lengths form a Pythagorean
triple? Explain.
a. Yes, they form a Pythagorean triple; 92 + 402 = 412 and 9, 40, and 41 are all
nonzero whole numbers.
b. No, they do not form a Pythagorean triple; although 92 + 402 = 412,
the side lengths do not meet the other requirements of a Pythagorean
triple.
c. No, they do not form a Pythagorean triple; 92 + 402 ≠ 412.
d. Yes; they can form a right triangle, so they form a Pythagorean triple.
28. Find the length of the hypotenuse.

a. 12 c. 5
b. 6 d. 18

29. Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.

a. 3.3 c. 24.7
b. 3.1 d. 8.5
30. Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.
 a. 6.2 cm c. 15.5 cm
b. 12.7 cm d. 10.9 cm
31. Find the value of x. Round to the nearest tenth.

a. 12.5 c. 13
b. 10 d. 9.7
32. Find the value of x.

a. 12.9 c. 12.4
b. 8.5 d. 8.1
33. The angle of elevation of the top of the building at a distance of 50 m from its foot on a
horizontal plane is found to be 60 degrees. Find the height of the building.
a. 86. 6 c. 88. 6
b. 87. 6 d. 89. 6
34. The well-known geometric theorem that the sum of the squares on the legs of a right
triangle is equal to the square on the hypotenuse, in familiar algebraic notation, a 2 + b2 =
c2.
a. Pythagoras
b. Pythagorean
c. Pythagorean theorem
d. Pythagora theorem

35. Find r, use the Pythagorean theorem.

r
5

12

a. 14 c. 13
b. 15 d. 12
36. From the top of the tower 30 m height a man is observing the base of a tree at an angle of
depression measuring 30 degree. Find the distance between the tree and the tower.
a. 51.96 c. 53. 96
b. 52. 96 d. 54. 96
37. It is any triangle that is not a right triangle.
a. Isosceles triangle
b. Oblique triangle
c. Special triangle
d. Congruence triangle
38. It is a triangle in which one angle is a right angle.
a. Isosceles triangle
 b. right triangle
c. Special triangle
d. Congruence triangle
39. The relationship between the sides and angles of non-right (oblique) triangles.
a. Law of sines
b. Law of cosine
c. Law of tangent
d. Law of secant
40. It is used to find the remaining parts of an oblique (non-right) triangle when either the
lengths of two sides and the measure of the included angle is known (SAS) or the lengths
of the three sides (SSS) are known.
a. Law of sines
b. Law of cosine
c. Law of tangent
d. Law of secant
41. Give the values of the Cos A of a right triangle measure 8cm for short leg and 17 for
hypotenuse.
15 17
a. c.
17 15
15 8
b. d.
8 17
42. A triangle has two sides with lengths of 15 and 9. The measure of the angle opposite the
latter is 34°. How many triangles can be formed?
a. 3 triangles c. 1 triangle
b. 2 triangles d. 4 triangles

43. A triangle has two sides with lengths of 17 and 19. The measure of the angle opposite the
latter is 5°. How many triangles can be formed?
a. 3 triangles c. 1 triangle
b. 2 triangles d. 4 triangles
44. A triangle has two sides with lengths of 63 and 75. The measure of the angle opposite the
side with a length of 75 is 22°. Find the measures of the angle opposite the side with a
length of 63 to the nearest degree.
a. 18° c. 20°
b. 19° d. 21
45. Simplify cos 80°
a. 0.23 c. 0.20
b. 0.17 d. 0.19
46. What is sin 75°?
a. 0.97 c. 0.87
b. 0.98 d. 0.88
47. For triangle ABC, a = 6, b = 10, and m<A = 42 degrees, how many triangles can be
formed?
a. One c. None
b. Two d. Three
48. For triangle DEF, d = 25, e = 30, and m<D = 40 degrees, Find measurements of f to
the nearest whole number.
a. 39 c. 59
b. 49 d. 69
49. What is sin 38°?
a. 0.62 c. 0.64
 b. 0.63 d. 0.65
50. What is cos 58°?
a. 0.53 c. 0.55
b. 0.54 d. 0.56