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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