Transcript angle of elevation - Brookwood High School

Questions from Homework??
Warm – up
Find the missing measures. Write all
answers in radical form.
y
x
60
45
x6
y3 3
z3 2
30
45
60°
y
10
30°
z
z
z 5 3
y 5
The Trigonometric Functions
SINE
Pronounced like “sign”
COSINE
Pronounced like “co-sign”
TANGENT
Pronounced “tan-gent”
B
With
Opp
A Respect to angle A,
Sin(A)  label the three sides
Hyp
Adj A
Cos(A) 
Hyp
Opp A
Tan(A) 
Adj A
A
C
B
With Respect to angle B, give
each ratio using X, Y and Z.
Sin(B)  X
Z
Y
Cos(B)  Z
A
Tan(B) 
X
Y
C
History of Trig Ratios
A young brave, frustrated by his inability to understand
the geometric constructions of his tribe's battle dress,
kicked out in anger against a stone and crushed his big
toe. Fortunately, he learned from this experience, and
went on to become the greatest man in the tribe.
However, because he was troubled throughout his life by
the problematic toe he acquired in his youthful fit, he was
constantly at the edge of the river, soaking his big toe in
the cooling waters. For that behavior, he was named …
Chief Soh Cah Toa.
Now the Chief
is famous for
his discoveries.
His name lives on to help us
remember our ratios.
SOH
CAH
O
sin( x) 
H
A
cos( x) 
H
TOA
O
tan( x ) 
A
Find the sine, the cosine, and the tangent of M.
Give a fraction and decimal answer (round to 4 places).
opp
9
sin M 

hyp
10.8  .8333
N
9
P
10.8
6
M
adj  6
cos M 
hyp 10.8  .5556
9
opp

tan M 
adj
6
 1.5
A
Find the sine,
cosine, and the
tangent of angle A
24.5
8.2
C
23.1
Give a fraction
and decimal
answer.
Round to 4 decimal
places
B
23.1
opp

sin A 
 .9429
24.5
hyp
adj
cos A 
hyp
8 .2

 .3347
24.5
opp
tan A 
adj
23.1
 2.8171

8 .2
Using a Calculator to Find
Values of Trig Functions
You can simply use the sin,
cos and tan buttons on the
calculator followed by the
degree measure of the
angle.
Sin (38º)
sin
)
38to change to degrees
Use your mode button
A word to the wise: Always make sure your calculator
is in the right mode for the type of angle you have
(degrees or radians)
Ex: 1 Find x. Round to the nearest tenth.
Figure out which ratio to use.
What we’re looking for…
What we know…
opp
tan 
adj
55
20 m
adj
x
opp
Ex: 2 Find the missing side.
Round to the nearest tenth.
x
283 m
24
x  115.1 m
Ex: 3 Find the missing side.
Round to the nearest tenth.
40
20 m
x
x  15.3 m
Ex: 4 Find the missing side.
Round to the nearest tenth.
80 m
72
x
x  26 m
Find the height h of the lamppost to
the nearest inch.
Ex. 5
A person is 200 yards from a river. Rather than walk
directly to the river, the person walks along a straight
path to the river’s edge at a 60° angle. How far must
the person walk to reach the river’s edge?
200
60°
x
Ex: 6
A surveyor is standing 50 metres from the
base of a large tree. The surveyor measures
the angle of elevation to the top of the tree
as 71.5°. How tall is the tree?
?
71.5°
50 m
For some applications of trig,
we need to know these meanings:
angle of elevation and
angle of depression.
Angle of Elevation
If an observer looks UPWARD toward
an object, the angle the line of sight
makes with the horizontal.
Angle of
elevation
Angle of Depression
If an observer looks DOWNWARD toward
an object, the angle the line of sight
makes with the horizontal.
Angle of
depression
You are skiing on a mountain with an altitude of 1200
meters. The angle of depression is 21o. About how far
do you ski down the mountain?
ANSWER You ski about 3348 meters down the mountain.
You want to build a skateboard ramp with a length of
14 feet and an angle of elevation of 26°. You need to
find the height and length of the base of the ramp.
ANSWER
The height is about 6.1 feet.
Homework!!! Yeah!!
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