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# Trigonometry and triangles

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Trigonometry and triangles

Trigonometry and triangles

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• There is a couple ways to do the first problem. Then can use Pythagorean theorem.

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• 1. Trigonometry and Triangles
Michael Schmidt
• 2. Trigonometry
Sine Cosine Tangent
Length of triangle legs
Angle of triangle corners
Area of triangles
What we are doing
• 3. Branch in Mathematics
Uses trig functions
Triangles
Mostly right triangles
Uses relationships to find unknowns
Trigonometry
• 4. θ (Theta)
Opposite leg (O)
Hypotenuse (H)
Key Terms
H
O
θ
A
• 5. SOH: sin θ =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
CAH: cos θ =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
TOA: tan θ =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡

SOH CAH TOA
• 6. sin 37° =
cos37° =
tan 37° =
SOH CAH TOA continued
21𝑓𝑡35𝑓𝑡
28𝑓𝑡35𝑓𝑡
21𝑓𝑡28𝑓𝑡

35ft
21ft
37°
28ft
• 7. What is given?
Which trig function?
Finding the side length
12ft
sin 30° = 𝑋12𝑓𝑡

X
sin 30°1 = 𝑋12𝑓𝑡

X= 6ft
30°
• 8. Using trig, find unknown
tan 20° = 𝑋6𝑚

1

X
X= 2.18m
20°
6m
X
cos 45° = 8𝑖𝑛𝑥

1

45°
X= 11.31in
8in
• 9. What is known?
tan θ = 34
Use 𝑡𝑎𝑛−1
𝑡𝑎𝑛−1( 34 ) = θ
θ = 36.86°

Using trig to find θ
3’
θ
4’
• 10. sin θ = 10𝑚15𝑚
𝑠𝑖𝑛−1(10𝑚15𝑚 ) = θ
θ = 41.81°

Solve for θ
θ
15m
10m
cos θ = 7𝑐𝑚9𝑐𝑚
𝑐𝑜𝑠−1(7𝑐𝑚9𝑐𝑚 ) = θ
θ = 38.94°

9cm
θ
7cm
• 11. Area of triangle
A = 𝐵𝐻2
A = 15∗102 = 75𝑚2

Finding the Area
10m
15m
• 12. What is given?
What is needed?
How is it found?
tan60 = 𝐵10
A =17.32𝑐𝑚∗10𝑐𝑚2

Finding area with trig
60°
10cm
B =17.32cm
=86.6𝑐𝑚2

• 13. Given
Needed
sin50 = 𝐻11
A= 13∗8.432

Non right triangles
H= 8.43in
11in
A=54.8𝑖𝑛2

50°
13in
• 14. cos 60 = 𝐻22
Pythagorean theorem for the base
A= 19.05∗112

Find area of triangle
H=11in
60°

22in
A=104.78𝑖𝑛2

• 15. Given
Needed
B= X+Y
tan 45 = 𝑥16
tan 30 = 𝑦16
B=25.24cm

Find area of triangle continued
Height = 16cm
16cm
45°
30°
X
Y
X=16cm
Y=9.24cm
A=16∗25.242

=201.92𝑐𝑚2

• 16. 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
tan 60 = 𝐿6

L=10.39ft
60°
6ft
L
• 17. Story problems
There 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?
sin 52 = 𝐻40
H=31.52ft

40ft
No, the ladder will not reach the window.
52°
• 18. SOH CAH TOA is key
Find the Given and Needed
Make own right triangle
Draw a picture
Wrap up