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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