Trigonometry and triangles

Trigonometry and triangles

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 ) Adjacent leg (A) Opposite leg (O) Hypotenuse (H ) Key Terms H O A θ

5. SOH: sin θ = CAH: cos θ = TOA: tan θ =   SOH CAH TOA

6. sin 37° = cos 37° = tan 37° = SOH CAH TOA continued 35ft 28ft 21ft 37°  

7. What is given? Which trig function? Finding the side length 12ft X 30° sin 30° =   =   X= 6ft

8. Using trig, find unknown 6m X 20° tan 20° =     cos 45° =     X 8in 45° X= 11.31in X= 2.18m

9. What is known? tan θ = Use ( ) = θ θ = 36.86°   Using trig to find θ 4’ θ 3’

10. sin θ = ) = θ θ = 41.81°   Solve for θ 15m 10m 9cm 7cm θ θ cos θ = ) = θ θ = 38.94°  

11. Area of triangle A = A = =   Finding the Area 10m 15m

12. What is given? What is needed? How is it found? = A =   Finding area with trig 10cm 60° B =17.32cm =86.6  

13. Given Needed = A=   Non right triangles 13in 11in 50° H= 8.43in A=54.8  

14. cos 60 = Pythagorean theorem for the base A=   Find area of triangle 22in 60   H=11in A=104.78  

15. Given Needed B= X+Y tan 45 = tan 30 = B=25.24cm   Find area of triangle continued 45° 30° Height = 16cm 16cm X Y X=16cm Y=9.24cm A =   =201.92  

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 60° 6ft L tan 60 =   L=10.39ft

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? 52° 40ft sin 52 = H=31.52ft   No, the ladder will not reach the window.

18. SOH CAH TOA is key Find the Given and Needed Make own right triangle Draw a picture Wrap up