Summative Test Trigonometry

QUEZON NATIONAL HIGH SCHOOL Ibabang Iyam Lucena City SUMMATIVE TEST Name: _________________________________________________________________ K_______ P_______ U_______ Section: ________ Date: ___________________________

Score:

DIRECTION: Blacken the circle that corresponds to the best answer I. KNOWLEDGE: A B C D ⃝ ⃝ ⃝ ⃝ 1. It is the angle from the horizontal line to the line of sight of the observer to the object below. a. Right angle c. Angle of Depression b. Angle of Elevation d. Special Angle ⃝ ⃝ ⃝ ⃝ 2. The side next to the reference angle is a right triangle is called _______. a. Adjacent Side b. Opposite Side c. Hypotenuse d. All of the above ⃝ ⃝ ⃝ ⃝ 3. With respect to the given angle, which among the following represents the ratio of the hypotenuse to the opposite side? a. Sine b. Cosine c. Tangent d. Cosecant ⃝ ⃝ ⃝ ⃝ 4. Given the figure on the right, which refers to the angle of depression? a.

∠ MKN

b.

∠ MKL

c.

∠ LKN

d. none of these ⃝ ⃝ ⃝ ⃝ 5. Evaluate: 2 sin 30o + tan 45o

√2

a.

b. 0

c.

√3

d. 1

⃝ ⃝ ⃝ ⃝ 6. This law states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus the product of these sides and the cosine of their included angle. a. Law of Cosines c. Law of Tangents b. Law of Sines c. Pythagorean Theorem ⃝ ⃝ ⃝ ⃝ 7. Determine the correct formula for tan ratio of angle

a.

length of side opposite ¿ tan θ=¿ angleθ c. length of hypotenuse

b.

length of side opposite length of hypotenuse tan θ= angleθ ¿ ¿

θ .

length of side opposite length of side adjacent tan θ=¿ angleθ ¿ angleθ ¿ ¿

d.

length of side adjacent ¿ tan θ=¿ angleθ length of hypotenuse

⃝ ⃝ ⃝ ⃝ 8. Given the figure at the right, which refers to the angle of elevation? a.

∠BCD b.

∠ ABC

c. both

∠ ABC

and

∠ BCD

d. None of the Above

II. PROCESS ⃝ ⃝ ⃝ ⃝ 1. ABCD is a rhombus with a side 7cm long. If longer diagonal.

m∠ A=13 0

∘

, find the length of its

a. 12.7 cm

b. 12.6 cm

c. 12.5 cm

d. 12.4 cm

Use the figure at the right to answer item numbers ⃝ ⃝ ⃝ ⃝ 2. Find x. a. 10 21.5

b. 14.1

⃝ ⃝ ⃝ ⃝ 3. Find y. a. 10

c. 17.3

b. 11.5

⃝ ⃝ ⃝ ⃝ 4. In triangle DEF, what is o

a. 35 b. 36o

d. 39o

c. 15.2

m∠ E

c. 54

d. 35

o

d. 17.3

to the nearest degree?

o

⃝ ⃝ ⃝ ⃝ 5. If p = 40 and q = 70, what is the measure of a. 34o b. 55o

d.

∠R ?

c. 30o

⃝ ⃝ ⃝ ⃝ 6. Find the longest side c to the nearest unit. a. 37 c. 28 b. 31 d. 29 ⃝ ⃝ ⃝ ⃝ 7. Which of the following statements is incorrect? a. b.

tan 60 °=

b 5

c. a = 10

sin 30 °=

5 a

d.

cos 60 °=

4 b

⃝ ⃝ ⃝ ⃝ 8. In right triangle ABC, AB = 16 cm and BC = 9cm. What is cos

8 9

a.

1

b. 2

c.

C ?

9 16

d.

16 9 ∠A

∆ ABC , AB = 9 cm and BC = 11 cm. Determine the tangent ratio of

⃝ ⃝ ⃝ ⃝ 9. In

to nearest hundredths. a. 0.64 b. 0.73 c. 1.36 d. 1.22 ⃝ ⃝ ⃝ ⃝ 10. In right triangle ABC, BC = 8 cm and AC = 17 cm. Find the value of sin C. a.

15 17

b.

17 15

c.

17 8

d.

8 17

III. UNDERSTANDING ⃝ ⃝ ⃝ ⃝ 1. The expression 3(sin 30o) – tan 45o is equal to. a. -0.5 b.0 c. 0.5

d. 1

⃝ ⃝ ⃝ ⃝ 2. A kite held by 100m of string makes an angle of elevation with the ground of 45o. About how high is the kite above the ground. a. 70.7 m b. 141.4 m c. 100 m d. 2.22 m ⃝ ⃝ ⃝ ⃝ 3.

∠Z

∆ XYZ is a non – right triangle. If XY measures 13 cm, XZ measures 9cm and

measures 25o then what is the measure of a. 17.01o

b. 51.14o

∠Y ? c. 17.89o

d. 24.58o

⃝ ⃝ ⃝ ⃝ 4. Two points A and B on the same side of a river are 15m apart. A tree on the opposite side of the river is directly opposite a point between A and B. The lines of sight of a tree across the river make angles 65 o and 53o, respectively, with the line joining A and B. Find the distance from point B to the tree. Express your answer to the nearest meter. a. 14 m b. 15m c. 16 m d. 17 m ⃝ ⃝ ⃝ ⃝ 5. A balloon is 45 m high. Its angle of elevation from observer A is 37 o and from observer B is 49o. What is the maximum distance between the two observers? Express your answer to the nearest meter? a. 98 m b. 99 m c. 100 m d. 101 m ⃝ ⃝ ⃝ ⃝ 6. Two ships leave the same port at the same time. One ship sails on a course of 110o at 32 mi/h. The other sails on a course of 230 o at 40 mi/h. find the distance between them after 2 hours. Express your answer to the nearest mile. a. 124 mi. b. 125 mi. c. 126 mi. d. 127 mi. ⃝ ⃝ ⃝ ⃝ 7. A triangular field has sides 500 feet, 450 feet, and 720 feet. Find the measure of the angle between the sides measuring 500 feet and 720 feet. Round off your answer to the nearest degree. a. 37o b. 38o c. 39o d. 40o ⃝

⃝

⃝

⃝

8. Two roads intersect at an angle of 100 o. Mildred’s mailbox is 8 m from the intersection. Jacque’s mailbox is on the other road and is 12 m from the intersection. How far is Jacque’s mailbox from that of Mildred’s? a. 14.99 m b. 15.45 m c. 15. 35 m d. 15.54 m

⃝ ⃝ ⃝ ⃝ 9. A surveyor finds that the angle between the base and the top of a flagpole on top of a building is 7o when the measurement is made from a point 150 feet from the base of a building. If the building is 100 feet tall, what is the height of the flagpole? Round off your answer to the nearest feet. a. 29 ft. b. 28 ft. c. 27 ft. d. 26 ft. ⃝ ⃝ ⃝ ⃝ 10. A lighthouse 20 m high with the base at sea level is sighted by a ship. If the angle of elevation from the ship to the top of the lighthouse is 12 o, what is the distance from the ship to the lighthouse? Round off your answer to the nearest meter. a. 92 m. b. 93 m. c. 94 m. d. 95 m. ⃝ ⃝ ⃝ ⃝ 11. A surveyor sights two signs and the angle between the two lines of sight measures 55o. If the first and the second signs are 70 m and 50 m away, respectively, from the surveyor, find the distance between the two signs. Express your answer to the nearest meter. a. 56 m b. 57 m c. 58 m d. 59 m ⃝ ⃝ ⃝ ⃝ 12. 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. 19o b. 20o c. 21o d. 22o

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