8-3 trigonometry. trigonometry trigonometry (trig) is used to find missing angles and sides of a...
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8-3 Trigonometry
Trigonometry
• Trigonometry (Trig) is used to find missing angles and sides of a right triangle
• There are 3 common trig functions– Sine = sinθ– Cosine = cosθ– Tangent = tanθ
θ = theta symbol for angle
Remember!!!!!!!!
• Hypotenuse – the longest side (across from the largest angle)
• Leg – the two sides of a right triangle forming the right angle– Adjacent Side – side next to
the angle– Opposite Side – the side
across from the angle
θ
Hypo
tenu
se
Adjacent to θ
Opposite of θ
Trig Functions
sinθ = opposite hypotenuse
cosθ = adjacent hypotenuse
tanθ = opposite adjacent
θ
SOH CAH TOAsinθ = opposite
hypotenuse
cosθ = adjacent
hypotenuse
tanθ = opposite
adjacent
What does an Indian do when they stub their toe?
They “soh cah toa”
Example 1
Find the value of x.
1) 2) 70°
x
8
60°
x10
Inverse of Trig Functions
θ = sin-1 opp hyp
θ = cos-1 adj hyp
θ = tan-1 opp adj
( )( )
( )
Calculator!!!!2nd sin2nd cos2nd tan
Example 2
Find the value of θ.
1) 2)θ 12
8
θ6
18
Find the Missing Angle or Side
1016
x
x
16
12
17x
9.7x
24
32
1.
4.3.
2.
The chair lift at a ski resort rises at an angle of 20.75° and attains a vertical height of 1200 feet.
• How far does the chair lift travel up the side of the mountain?
d1200
20.75°
Example 3
• A film crew in a helicopter records an overhead view of a skier’s downhill run from where she gets off the chair lift at the top to where she gets back on the chair lift for her next run. If the helicopter follows a level flight path, what is the length of that path.
d
1200
20.75°
---------------------------------
Example 4
Angles of Elevation and Depression
Angle of elevation – the angle between a horizontal line and the line of sight from an observer to an object at a higher level.Angle of depression – angle to an object at a lower angle.
Example 5
• John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle of elevation to the top of the tree is 33º . How tall is the tree?
Example 6
• A building is 50 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41º. How far is the observer from the base of the building?
Example 7
• An airplane is flying at a height of 2 miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport?