trigonometry and triangles
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Trigonometry and Triangles
Michael Schmidt
Trigonometry
Sine Cosine Tangent
Length of triangle legs
Angle of triangle corners
Area of triangles
What we are doing
Branch in Mathematics
Uses trig functions
Triangles
Mostly right triangles
Uses relationships to find unknowns
Trigonometry
θ (Theta)
Adjacent leg (A)
Opposite leg (O)
Hypotenuse (H)
Key Terms
H
O
A
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°X= 6ft
Using trig, find unknown
6m
X
20°
X
8in45°X= 11.31in
X= 2.18m
Using trig to find θ
4’θ
3’
Solve for θ
15m
10m
9cm
7cm
θ
θ
Finding the Area
10m
15m
Finding area with trig
10cm
60°
B =17.32cm
Non right triangles
13in
11in
50°
H= 8.43in
Find area of triangle
22in
H=11in
Find area of triangle continued
45° 30°
Height = 16cm
16cm
X Y
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
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°
40ft
No, 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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