SUMMATIVE TEST IN MATH 9
QUARTER 4
Name: _____________________________
__________
Yr.
&
Section:
_____________________Date:
Directions: Read each item carefully. Choose the letter that corresponds to the best answer and write
it
on your answer sheet.
1. Determine the correct formula for the tan ratio of
a. tan B = length of side adjacent B
length of the hypotenuse
B.
c. tan B =
length of hypotenuse
length of side opposite to
B
b. tan B = length of side opposite to B d. tan B = length of side opposite to B
length of side adjacent to B
length of hypotenuse
2. The trigonometric ratio sine is the reciprocal of what trigonometric ratios ?
a. sine
b. cosine
c. tangent
d. cosecant
3. Which of the following does NOT belong to the six trigonometric ratios?
a. sine
b. hypotenuse
c. secant
d. tangent
𝑠𝑖𝑛𝜃
4. What trigonometric ratio can be represented by 𝑐𝑜𝑠𝜃 ?
a. secant
b. cosecant
c. tangent
d. cotangent
5. In ∆ ABC , AB = 9 cm and BC = 11 cm. Determine the tangent ratio of ∠A to the
nearest hundredths.
a. 0.64
b. 0.73
D
c. 1.36
d. 1.22
6. With respect to the given angle, what is the ratio of the hypotenuse to the opposite side?
a. sine
b. cosine
c. tangent
d. cosecant
7. Which statement is incorrect?
a. The hypotenuse is the longest side in a right triangle.
b. The hypotenuse is always the opposite side of the 90o in a right triangle.
c. The Pythagorean theorem applies to all right triangles.
d. You can solve for the unknown side in any triangle, if you know the lengths of
the other two sides, by using the Pythagorean theorem.
8. From triangle ACB, with right angle at C, if b = 15 and c = 30, what is the measure
of ∠B?
a. 40o
b. 30o
c. 60o
d. 45o
9. The missing parts of a right triangle with the given two parts can be solved using
a. Pythagorean
b. law of sines
c. SOH-CAH-TOA
d. both a and c
10. Which is equivalent to sec 𝜃?
a.
1
cos 𝜃
b.
1
c.
secθ
11. If g = 40 and e = 80, what is the measure of ∠F?
a. 40°
c. 60°
b. 55°
d. 65°
1
1
sin 𝜃
d.
1
tanθ
12. If p = 20 and q = 50, what is the measure of ∠R?
a. 46.62°
c. 66.42°
b. 52.64°
d. 76.24°
For nos. 13-15, refer to the figure at the right.
13. Which of the choices below best illustrates for
the tan ratio of 53° ?
a. tan 53° =
s
t
c. tan 53° = s
t
p
b. tan 53° = s
d. tan 53° =
p
t
14.
14. Which of the choices below best illustrates for the csc ratio of 53° ?
a. csc 53° =
p
t
b. csc 53° =
s
c. csc 53° =
p
t
p
d. csc 53° =
s
t
15. Which is the correct value of p if t = 50 ?
a. 23.93
b.
39.93
c.
53.33
d. 93.39
16. In a special right triangle 45°-45°-90° of triangle ACB with right angle at C,
which equation is NOT TRUE?
a. b = a
b. c = a
17. Solve for sec 60o – cos 0o.
a.
c. a =
𝑐 √2
2
c. ½
b. 1
d. c = a
d. 2
18. Given the figure on the right, which refers to the angle of depression?
a. ∠MKN
c. ∠LKN
b. ∠MKL
d. none of these
19. What is the value of x?
a. 3
c. 6
b. 3√2
d. 6 √2
20. A kite held by 125 m of string makes an angle of elevation with the ground of 45°. About how
high is the kite above the ground?
a. 62.8 m
b. 75.1 m
c. 88.4 m
d. 113.6 m
21. From the top of a barn 7.62 m high, you see a cat on the ground. The angle of depression of
the cat is 40°. How many meters must the cat walk to reach the barn?
a. 9.08 m
b. 9.80 m
c. 9.81 m
d. 9.18m
22. With the sun, a girl 1.4 m tall casts a 3.6 m shadow. Find the angle of elevation from the tip of
the shadow to the sun. Express your answer to the nearest degree.
a. 19°
b. 20°
c. 21°
d. 22°
23. The expression 2(sin 30°) – tan 45° is equal to
a. 0
b. 1
c. 2
d. –1
24. The angle from the horizontal to the line of sight of the observer to the object above.
a. angle of depression
c. angle of elevation
2
b. horizontal angle
d. oblique angle
o
o
o
25. Evaluate: 2 sin 30 + 4cos 60 – 3 cot 45 + sec 45o .
a . √2
b. 0
c . √3
d. 1
o
o
o
26. In a special right triangle 30 -60 -90 of triangle ACB with right angle at C,
which equation is correct?
a. c = a
b. b = a
c. a = b
d. c =2a
27. A 10-foot ladder is placed so as to form an angle of 25° with the wall of a building. How
far
is the ladder from the base of the building?
a. 4.1 ft.
b. 4.2 ft.
c. 4.4 ft.
d. 4.5 ft.
28. An imaginary line that connects the eye of an observer to the object being observed.
a. horizontal line
b.. vertical line
c. line of the observer d.
line of sight
o
29. Find the value of tan 45 .
a. ½
b.
c.
d. 1
30. Solve for 2(sin 30o ) + tan 45o.
a.
+1
b. 2 +
c. 2
d. 3
31. Which of the following is used to solve for side b in the diagram shown at the
right?
a) sine
b) cosine
c) tangent
d. cosecant
32. What is used to solve x in the figure below?
a) sine
b) cosine
c) tangent
d. cotangent
33. With respect to the given angle, what is the ratio of the hypotenuse to the opposite side?
a. sine
b. cosine
c. cotangent
d. cosecant
34. Which of the following statement is correct?
𝑦
x
a. x = 6
c. sin 60˚ =
60
𝑥
4
1
4
˚
b. sin 30˚ = 𝑥 d. sin 30˚ = 𝑦
y
35. Given the figure on the right, which refers to the angle of depression?
a. ∠MKN
c. ∠LKN
b. ∠MKL
d. none of these
36. Using the same figure at the right, which refers to the angle of elevation?
a. ∠MKN
b. ∠MKL
c. ∠LKN
d. none of these
37. In right triangle PQR, PQ = 12 cm and QR = 5 cm. What is cot R?
a.
12
13
b.
5
13
c.
5
d.
12
12
5
38. Refer to the same problem in No. 6, what is cos R?
a.
12
13
b.
5
13
c.
5
d.
12
12
5
39. What is sin P?
a.
12
13
b.
5
13
c.
5
d.
12
40. What is sec P?
3
12
5
a.
13
12
b.
5
13
c.
5
d.
12
12
5
41. A newlywed couple wants to purchase a piece of land which is triangular in shape. If the two sides
of the lot measure 25 m and 30 m and their included angle is 60o, what is its area? (sin 60˚ = 0.8660)
a.243.57 m2
b. 324.75 m2
c. 432.57 m2
d. 572.34 m2
42. Find x using the law of sines from the given figure. (sin 60˚ = 0.8660, sin 45˚ = 0.7071)
a. 8.90 cm
b. 9.20 cm
x
12 cm
c. 9.80 cm
d. 9 cm
60o
45o
43. Find the length of AB from the given figure. Round off to the nearest tenth.
a. 25.2 units
b. 21.2 units
c. 20.2 units
d. 22.2 units
44. A kite held by 125 m of string makes an angle of elevation with the ground of 45°. About how high
is the kite above the ground? (sin 45˚ = 0.7071)
a. 62.8 m
b. 75.1 m
c. 88.4 m
d. 113.6 m
45. A flagpole 18 feet tall casts a shadow of 12 feet long at a specific time of day. Find, to the nearest
degree, the angle of elevation of the sun at this time of day.
a. 56º
b. 48º
c. 42º
d. 34º
Prepared by:
Noted by:
Glaiza P. Javier
School Teacher III
Jonathan J. Molina
Principal II
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