Transcript Trigonometry

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You have
completed
the EOCT!
Warm Up #1
Warm Up #2
City of Atlanta
Solution
Extension Assignment (HW)
Trigonometry
DERIVED FROM THE
ANCIENT GREEK
LANGUAGE AND
MEANS THE
MEASUREMENT OF
TRIANGLES.
Measurement of Triangles
Sides
Angles
Ways we already
know:
 Pythagorean
Ways we already
know:
 Triangle Sum
Theorem
 Congruent
Triangles
 Similar Triangles
Theorem
 Congruent
Triangles
 Similar Triangles
Vocabulary we need…
Vocabulary we need…
Labeling a right triangle
For any right triangle , six ratios of pairs of
sides are possible.
a
c
,
b
c
,
a
b
,
b
a
,
c
a
,
c
b
This year we will study
3 of the ratios.
Sine ratio
 The sine of A …
sin( A ) 
length of side opposite
A

length of hypotenuse
a
c
 The sine of B …
sin( B ) 
length of side opposite
length of hypotenuse
B

b
c
Ex.1 In ∆ ABC, find the following…
sin( A ) 
8
17
sin( B ) 
15
17
Cosine ratio
 The cosine of A …
cos( A ) 
length of side adjacent to
A

hypotenuse
b
c
 The cosine of B …
cos( B ) 
length of side adjacent to
hypotenuse
B

a
c
Ex.2 In ∆ ABC, find the following…
cos( A ) 
cos( B ) 
15
17
8
17
Tangent ratio
 The tangent of A …
tan( A ) 
length of side opposite
A
length of side adjacent
A

b
 The tangent of B …
tan( B ) 
length of side opposite
B
length of side adjacent
B
a

b
a
Ex.3 In ∆ ABC, find the following…
tan( A ) 
8
15
15
tan( B ) 
8
A little help to remember….
SOHCAHTOA
 SOH - Sine , Opposite leg, Hypotenuse
 CAH - Cosine , Adjacent leg, Hypotenuse
 TOA - Tangent, Opposite leg, Adjacent leg
Let’s practice…
Using angle measures
 Since corresponding sides of similar
triangles are proportional, the sine ratio
is the same in any right triangle. This is
true for any trigonometric value of an
angle in a right triangle. The values for
any angle measures can be found using a
calculator.
sin A 
sin D 
Calculators
 Make sure that your
calculator is in degree
mode
sin 43  
0.6820
tan 57  
1.5399
cos 71   0.3256
You can find the measure of an angle if one of
its trigonometric values is known.
Example 1 :
cos A  0.5592
1
cos (0.5592 ) 
Example 2:
sin A 
2
3
sin
1
2
 
3
Guided Practice
 Making Practice Fun 82
Solving Right Triangle Problems
 In ∆ ABC , m<B = 61°, c = 20, find b.
b = 17.5
Solving Right Triangle Problems
 In ∆ ABC , m<B = 42°, c = 10, find b.
b = 6.7
Solving Right Triangle Problems
 In ∆ ABC , m<A = 39°, b = 20, find a.
a = 7.3
Finding an angle measure
 Find the m<A?
What trig
function?
23.9°
Angle of Elevation/ Angle of Depression
The angle of elevation of an airplane is 12°. The
distance to the plane is 16 km. How high is the
plane?
3.3 km
A fire warden’s tower is 43 m tall. The angle of depression from the
window of the tower to a fire in the woods is 5°. How far away from the
base of the tower is the fire?
491 m
Guided practice
 1. A kite is flown with 210 m of string. The angle of
elevation of the kite is 61°. How high is the kite?
 2. The top of a lighthouse is 110 m above the level of
the water. The angle of depression from the top of
the lighthouse to a fishing boat is 18°. How far is the
base of the lighthouse is the fishing boat?
 3. A mountain trial slopes upward at an angle of 5°.
A hiker hikes four miles up the trail. How much
altitude does the hiker gain?
 187.3 m
338.6 m 0.35 km
Assignment
 Making Practice Fun 83
 “Big Grass Field” Puzzle