congrats! you have completed the eoct!. warm up #1
TRANSCRIPT
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Congrats!
You have completedthe EOCT!
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Warm Up #1
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Warm Up #2
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City of Atlanta
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Solution
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Extension Assignment (HW)
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DERIVED FROM THE ANCIENT
GREEK LANGUAGE AND MEANS THE
MEASUREMENT OF TRIANGLES.
Trigonometry
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Measurement of Triangles
Sides
Ways we already know:
Pythagorean TheoremCongruent Triangles Similar Triangles
Angles
Ways we already know:
Triangle Sum TheoremCongruent TrianglesSimilar Triangles
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Vocabulary we need…
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Vocabulary we need…
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Labeling a right triangle
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For any right triangle , six ratios of pairs of sides are possible.
b a b c , , , , ,
c b a b
a c
c a
This year we will study 3 of the ratios.
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Sine ratioThe sine of A …
The sine of B …
length of side opposite Asin( )
length of hypotenuse
aA
c
length of side opposite sin( )
length of hypotenuse
B bB
c
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Ex.1 In ∆ ABC, find the following…
sin( )A
sin( )B
8
1715
17
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The cosine of A …
The cosine of B …
length of side adjacent to Acos( )
hypotenuse
bA
c
length of side adjacent to cos( )
hypotenuse
B aB
c
Cosine ratio
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Ex.2 In ∆ ABC, find the following…
cos( )A
cos( )B
15
17
8
17
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The tangent of A …
The tangent of B …
length of side opposite tan( )
length of side adjacent
B bB
B a
length of side opposite Atan( )
length of side adjacent A
aA
b
Tangent ratio
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Ex.3 In ∆ ABC, find the following…
tan( )A
tan( )B
8
15
15
8
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A little help to remember….
SOHCAHTOASOH - Sine , Opposite leg,
HypotenuseCAH - Cosine , Adjacent leg,
HypotenuseTOA - Tangent, Opposite leg,
Adjacent leg
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Let’s practice…
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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.
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sin
sin
A
D
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CalculatorsMake sure that your
calculator is in degree mode sin 43
tan57
cos71
0.6820
1.5399
0.3256
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You can find the measure of an angle if one of its trigonometric values is known.
Example 1 :
Example 2:
1
cos 0.5592
cos (0.5592)
A
1
2sin
32
sin3
A
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Guided Practice
Making Practice Fun 82
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Solving Right Triangle Problems
In ∆ ABC , m<B = 61°, c = 20, find b.
b = 17.5
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Solving Right Triangle Problems
In ∆ ABC , m<B = 42°, c = 10, find b.
b = 6.7
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Solving Right Triangle Problems
In ∆ ABC , m<A = 39°, b = 20, find a.
a = 7.3
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Finding an angle measure
Find the m<A?
What trig function?
23.9°
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Angle of Elevation/ Angle of Depression
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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
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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
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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
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Assignment
Making Practice Fun 83
“Big Grass Field” Puzzle