CO-2-slides Its about Angle of Depression

MATHEMATIC
S 9
9-
kAMAGONG
May 31, 2023
2:30- 3:20 pm

Learning Competency
uses trigonometric ratios to
solve real-life problems
involving right triangles.
(solves real life problems
involving angle of
depression)
M9GE-IVe-1

Learning
objectives
01
02
03
sketch a diagram from a real-
world problem involving an angle
of depression and use this to
help solve the problem
use right triangle trigonometry to
solve real-life problems involving
the angle of depression
appreciate the importance of an angle
of depression as related to the real-
world problem solving.

SLIDESMANIA.C
Click on the balloon to go
back.
1) Which of the following is an example of a scenario
that illustrates angle of depression?
A. A cable man on a post looking at his service
car.
B. A point P on the ground and a flying airplane.
C. Romeo serenading Juliet at the window of a two
– storey house.
D. A sailor at the sea looking at the top of the
lighthouse.

SLIDESMANIA.C
back.
2) In the figure below, which is the angle of
depression?
A. ∠1
B. ∠2
C. ∠3
D. ∠4

SLIDESMANIA.C
back.
3) A kite is flying at a height of The angle of depression made by the
kite to point P on the ground is . Find the length of string of the kite
that is attached to the ground. Which of the following best illustrates
the problem?
𝑥
A. C.
B. D.
𝑥
𝑥
𝑥
𝑥

SLIDESMANIA.C
Type the title here.
And the exit ticket prompt here.
back.
4) In the figure below, which of the following
angles also measures ?
𝑥
∠1 ∠2
∠3
A. ∠1
B. ∠2
C. ∠3
D. None of
the
above

SLIDESMANIA.C
back.
5) In solving a right triangle given an acute angle
provided by the angle of depression, what
trigonometric ratio should be used if the opposite
and the adjacent sides of the acute angle are
given?
A. C.
B. D.

CONGRATULATIO
NS!
You may claim me
after the tour!

Solving problems
involving Angle of
elevation and
angle of depression

Activity
1You and your friend have decided
to ride the Wheel of Fate in
Enchanted Kingdom. When you
reached the highest point of the
ride, you saw one of your
classmates standing near the

Activity 1
Process Questions:
1. What scenario illustrates an angle of depression?
2. Use a ruler to sketch the angle of depression.
3. When you reached the highest point of the Ferris
Wheel, it stopped. You used the school-made
clinometer to measure the angle of depression to
your classmate. Is it possible to get the height of the
Ferris wheel if you know the distance of your
classmate from the base of the Ferris Wheel?
4. What mathematical concept will you use to solve

EXAMPLE 1
The tower is 15.24 m high. At a
certain distance away from the tower, a
man on the level ground observes that
the angle of elevation to the tower’s top
is 41 degrees. How far is the man from
the tower?

EXAMPLE 1
Upon using the clinometer, the angle of depression
measures and the distance from your classmate to the
base of the Ferris Wheel is . What is the approximate height
of the Ferris Wheel to the nearest ?
1)Sketch the diagram with a
complete label based on the
given information in the
problem.

𝟔𝟖°
𝟔𝟖°
𝟓𝟐.𝟓 𝒇𝒕
𝒙
2) What figure is
formed?

𝟔𝟖°
𝟔𝟖°
𝟓𝟐.𝟓 𝒇𝒕
𝒙
3) What are the known
parts of the triangle?
How about the
unknown part?
measures
Adjacent side to
measures
Opposite side to is
unknown

𝟔𝟖°
𝟔𝟖°
𝟓𝟐.𝟓 𝒇𝒕
𝒙
4) What trigonometric
ratio is appropriate to
use to solve the missing
part of the triangle?
adjacent
opposite
tan 𝜃=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒𝑡𝑜𝜃
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒𝑡𝑜 𝜃

tan 68 °=
𝑥
52.5
52.5 ( tan 68 °)=𝑥
129.94=𝑥
𝑥=129.94
5)What is the approximate height of the
Ferris Wheel to the nearest feet?
The approximate height of the Ferris
Wheel is .

STEPS In solving problems involving angle of elevation and angle of
depression
Read and analyze the problem.
Identify the known and unknown values and part
of right triangle.
Sketch the diagram with label based on the given
information.
Determine the appropriate trigonometric
ratio and form an equation.
01
03
02
04
05 Solve the equation.
06 Answer the question in the
problem

EXAMPLE 1
You’re still at the highest point
of the Ferris Wheel, when your
classmate went to buy popcorn,
will the distance of your
classmate from the base of the
Ferris Wheel be the same?

EXAMPLE 1
How about the angle of
depression?

EXAMPLE 2
From a seat 130 ft high on a Ferris
Wheel, your classmate is away from
the base of the Ferris Wheel. Find the
angle of elevation in nearest degrees.

Step 2: Sketch the diagram with label
based on the given information.
𝜽
𝜽
𝟓𝟓 𝒇𝒕
𝟏𝟑𝟎 𝒇𝒕

𝜽
𝜽
𝟓𝟓 𝒇𝒕
𝟏𝟑𝟎 𝒇𝒕
is unknown
Adjacent side to
measures
Opposite side to
measures

𝜽
𝜽
𝟓𝟓 𝒇𝒕
𝟏𝟑𝟎 𝒇𝒕
Adjacent
Opposite
Step 4: Determine the appropriate trigonometric ratio and form an equation
tan 𝜃=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒𝑡𝑜𝜃
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒𝑡𝑜 𝜃
tan 𝜃=
130
55

tan 𝜃=
130
55
𝜃=tan− 1
(130
55 )
𝜃=67.0679
Step 5: Solve the
equation.
Step 6: Answer the question in the problem
Find the angle of depression in nearest degrees.
The angle of depression measures

EXAMPLE 3
Imagine you are riding the “EKstreme
Tower” at the amusement park. The tower
is tall. As you reach the top of the tower,
you look down and notice that the angle of
depression to the ice cream stand is 65°.
How far does the ice cream stand to the top
of the tower? Round off your answer to the
nearest hundredths.

𝟔𝟓°
𝟔𝟓°
𝟒𝟎𝒎 𝒙

𝟔𝟓°
𝟔𝟓°
𝟒𝟎𝒎 𝒙
measures
Opposite side to
measures
The length of the
hypotenuse is
unknown

𝟔𝟓°
𝟔𝟓°
𝟒𝟎𝒎 𝒙
hypotenuse
Opposite
sin 𝜃=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒𝑡𝑜 𝜃
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
sin 65=
40
𝑥

sin 𝜃=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒𝑡𝑜 𝜃
h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
sin 65°=
40
𝑥
𝑥sin 65°=40
sin 65° sin 65°
𝑥=48.3776

𝑥=48.3776
How far does the ice cream stand to the
top of the tower?
The ice cream stand is away to the top of
the tower?

Read and analyze the
problem. Follow the steps
in solving the problem
involving angle of
depression.
GROUP ACTIVITY!

THANK YOU
For your active
participation!

CO-2-slides Its about Angle of Depression

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