Transcript MATHEMATICS FORM 5

MATHEMATICS
FORM 4
ANGLES OF ELEVATION AND DEPRESSION
Hello there. How are you? Welcome back. Did you know
what we are going to learn today? Yes. We are going to
learnt about Angles of elevation and depression. However,
let’s us recall back what is angle. Do you know angles?
If you did not remember
about angles, let watch
this video together.
PLAY
VIDEO
Now, can you remember
what is angles? If yes,
good. But today we are
going to learn about
angles of elevation and
depression.
At the end of the lesson,
students will be able to:
Hi there. Here are
our learning
identify the horizontal line, the
objectives for today.
angle of elevation and the angle
of depression for a particular
situation
Represent a particular situation
involving angles of elevation
and depression using diagrams
Solve problems involving the
angle of elevation and the angle
of depression
Now, first let’s us
learn how to
identify the
horizontal lines,
angles of elevation
and angles of
depression.
Angle of elevation is the angle between the
horizontal line that passes through an
observer’s eye and the straight line that
joins the observer’s eye to an object
situated at the higher lever than the
observer.
What about the angle
of depression? Can
you guess it?
The angle of depression is the angle
between the horizontal line that
passes through an observer’s eye and
the straight line that joins the
observer’s eye to an object situated at
a lower level than the observer. By the
way? Can you tell me what is
horizontal line?
Now, do you
understand what is
angle of elevation and
angle of depression? If
no, let’s us take a look
on one diagram…
T
The diagram on the left
A
R
ANGLE OF ELEVATION
Q
ANGLE OF DEPRESSION
shows a tower DQT and a
building
AB
on
a
horizontal ground. A man
at the position R views
B
D
the peak of the tower T.
RQ is the horizontal line
The angle of depression of D from R is
∟QRD
The angle of elevation of T from R is
∟TRQ
QUESTION 1
QUESTION 2
BACK
B
P
A
In the diagram above, AB is a building on a horizontal ground.
Identify:
a) The horizontal line
ANSWER
b) The angle of elevation of B from P
ANSWER
NEXT
T
12.5 m
P
R
16 m
The above diagram shows a vertical pole TP on a horizontal
plane.
a) State the horizontal line
ANSWER
b) Find the angle of elevation of T from R
ANSWER
Sssstt…do you really
want to know the
answer? Well…the
answer is :
THE HORIZONTAL
LINE IS PA.
BACK TO QUESTION
1
Hmm….the correct answer is :
THE ANGLE OF ELEVATION
OF B FROM P IS APB
BACK TO QUESTION
1
The answer is :
THE HORIZONTAL LINE IS
PR.
BACK TO QUESTION
2
Well….the correct answer is :
THE ANGLE OF ELEVATION
OF T FROM R IS TRP
BACK TO QUESTION
2
Hi there. Did you
know how to
represent particular
situation involving
angles of elevation
and depression using
diagrams?
You
did
not
know?
Don’t
worry. I can help you. Here are
the steps:
1. Draw the positions of the
object and observer
2. Draw the horizontal line
3. Join the eye of the observer
and the object
4. Indicate the angle
Do you understand it? Ok..let’s us take a look on one examples ok? Here
the example:
PQ and RS are two vertical poles on a horizontal plane.
These poles are 10m apart. PQ is 9.5m while RS is 5m. The
angle of elevation of P from R is 25° and the angle of
depression of Q from R is 26°. Draw a labeled diagram to
represent this situation.
We give you 2
minutes to
try to answer
it. Ok? Good
Luck!
P
Here are the
answer. Check
25°
with your
R
26°
answer ok?
Q
S
How is it? Did your answer correct? Do you want to try one
more question ? Try answer this:
A vertical pole, TP, with a height of 5m is standing on
a horizontal ground PQR. PQR is 10m with PQ=QR.
The angle of elevation of vertex T from R is 27° and the
angle of elevation of vertex T from Q is 45°. Draw a
labeled diagram to represent this situation.
CHECK YOUR
ANSWER
T
Here is the
correct
answer…
45°
P
27°
Q
How’s your
performance? If
correct,
congratulation! If
not, don’t give up.
Try again.
NEXT
R
Hi there. I am Mr. Tiger..
Now we are going to learn
the last learning objevtives
of Angles of Elevation and
Depression topic. We will
now learn how to solve
problems involving angles
of elevation and
depression. Let’s go!!
Let us take a look on this question:
In the diagram below, represent a building
BC on a horizontal ground BA. The height
of the building is 37m. The angle of
depression of A from C is 65°. Calculate the
distance BA.
C
37m
B
A
Did you know how to solve it?
Let us watch this video first
and then try to answer the
question given earlier. Perhaps
this video can help you in order
to solve this question.
PLAY
VIDEO
Let us check the answer together:
C
65°
D
37m
B
xm
A
∟ACB = 90° - 65° = 25°
Tan 25° = x / 37
x = 37 tan 25°
= 17.25 m
# The distance of BA is 17.25 m
QUIZ
QUESTIONS
For more information on
angles of elevation and
depression click here.
HOMEWORK
PLAY ANGLES
GAME click here