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TrigonometryApplications of Trigonometry

Summative Test

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1.It is the acute angle which is formed by a horizontal line

and an observers line of sight to any object below thehorizontal

a. angle of elevation

b. angle of depression

c. oblique angle

d. complementary angles

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2. Two airplanes cross each other at an angle of 49. At a certain

instant, airplane A is 32 miles from the crossing, while airplane B

is 76 miles from the crossing. What is the distance between themat this instant.

a. 44 miles

b. 81 miles

c. 27 miles

d. 60 miles

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3. A helicopter hovers 250m directly above a small island

that is off the Cavite coast. From the helicopter, the pilot

takes a sighting to a point P directly ashore on the mainland

at the waters edge. If the angle of depression is 30, how far

off the coast is the island?

a. 216 meters

b.433 meters

c.125 meters

d. 250 3meters

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4. From the window 10 meters above the level ground, abuilding which is 40 meters high, and at a distance of 75

meters from the window, is observed, find the angle ofelevation from the window to the top of the top of the

building and the angle of depression from the window to the

base of the building.

a. 66 25 and 82 20 respectively

b. 2148 and 736 respectively

c. 23 34 and 739 respectively

d. 60 25 and 75 20 respectively

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5. Two ships leave a port at the same time. Ship A sails on a

course of N15E at 24 knots while ship B sails on a course N105E

at 7 knots. Find the distance between the ships after 1 hour.

a. 31 nautical miles

b. 17 nautical miles

c. 38 nautical miles

d.25nautical miles

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Congratulations..

The angle of depression is the acute angle which isformed by a horizontal line and an observers line of

sight to any object below the horizontal.

NEXT QUESTION

Line of depression

Horizontal Line

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Your choice is Incorrect...

Dont give up and try again.

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Good Job!!!..

We use cosine law to solve for the distance d between the two

airplanes. Thus,

= (32)+(76)2 32 76 cos 49

= 1024 + 5776 2 2432 0.6561

= 3608.73

= 3608.93

= 60.07

32 miles

76 miles

B

d

A

49

Next question

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Your choice is Incorrect...

Dont give up and try again.

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Well Done!!!

Solution: cot 30 =

= 250 cot 30

= 250 3meters

NEXT QUESTION

mainland x island

250 m

30

30

helicopter

P

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Your choice is Incorrect...

Dont give up and try again.

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You are correct!!!Solution:

i) Let be the angle of elevation to the top of the building, then

tan =30

75

=2

5

= 2

5

=2148

i) Let be the angle of depression to the base of the building, then

tan =

=

= 2

15=736

75

40

30

10

Next question

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Your choice is Incorrect...

Dont give up and try again.

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Absolutely!!!!

Click the arrow to go the main slide

End

Solution:

i) After 1 hour, the distance traveled by ship A is 24 nautical miles and the distance

traveled by the ship B is 7 nautical miles. From the figure, the 2 ships and the portform a right triangle. Thus, we can use the pythagorean theorem to solve for the

distance between the 2 ships.

= +

= (24)+ (7) = 576 + 49 = 625

= 625 = 25 n.m.

105

=?

7 n.m.

15

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Your choice is Incorrect...

Dont give up and try again.

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Great Job!! Keep it up!!

As long as you keep practicing,

Math will never be a hard

subject

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