trigonometry and triangles
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Trigonometry and Triangles
Michael Schmidt
TrigonometrySine Cosine Tangent
Length of triangle legs Angle of triangle corners Area of triangles
What we are doing
Branch in MathematicsUses trig functionsTriangles
Mostly right trianglesUses relationships to find unknowns
Trigonometry
θ (Theta)Adjacent leg (A)Opposite leg (O)Hypotenuse (H)
Key Terms
H
O
Aθ
SOH: sin θ =CAH: cos θ =TOA: tan θ =
SOH CAH TOA
sin 37° =
cos 37° =
tan 37° =
SOH CAH TOA continued
35ft
28ft
21ft
37°
What is given? Which trig function?
Finding the side length
12ft X
30°
sin 30° =
= X= 6ft
Using trig, find unknown
6m
X
20°
tan 20° = ❑1
cos 45° = ❑1
X
8in45°
X= 11.31in
X= 2.18m
What is known? tan θ = Use ( ) = θ θ = 36.86°
Using trig to find θ
4’θ
3’
sin θ = ) = θθ = 41.81°
Solve for θ
15m
10m
9cm
7cm
θ
θ
cos θ = ) = θθ = 38.94°
Area of triangleA =
A = =
Finding the Area
10m
15m
What is given?What is needed?How is it found?
=
A =
Finding area with trig
10cm
60°
B =17.32cm =86.6
GivenNeeded =
A=
Non right triangles
13in
11in
50°
H= 8.43in
A=54.8
cos 60 = Pythagorean theorem for the base
A=
Find area of triangle
22in
60
H=11in
A=104.78
GivenNeeded
B= X+Ytan 45 = tan 30 = B=25.24cm
Find area of triangle continued
45°
30°
Height = 16cm
16cm
X YX=16cm
Y=9.24cm
A= =201.92
A 6ft tall man is standing in front of a light. The light is casting a shadow. If the angle of depression at the man’s head is 60° how long is the shadow?
Story Problems
60°6ft
L
tan 60 = L=10.39ft
Story problemsThere is a window 33ft up a building and the only ladder is 40ft long. For safety reasons the ladder is leaned
against the building at 52°. Will the ladder reach the window?
52°
40ftsin 52 =
H=31.52ftNo, the ladder will
not reach the window.
SOH CAH TOA is key
Find the Given and Needed
Make own right triangle
Draw a picture
Wrap up
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