Your SlideShare is downloading. ×
0
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Trigonometry and triangles
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Trigonometry and triangles

148

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
148
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide
  • There is a couple ways to do the first problem. Then can use Pythagorean theorem.
  • Transcript

    • 1. Trigonometry and Triangles<br />Michael Schmidt<br />
    • 2. Trigonometry<br />Sine Cosine Tangent<br />Length of triangle legs<br />Angle of triangle corners<br />Area of triangles<br />What we are doing<br />
    • 3. Branch in Mathematics<br />Uses trig functions<br />Triangles<br />Mostly right triangles<br />Uses relationships to find unknowns <br />Trigonometry<br />
    • 4. ΞΈ (Theta)<br />Adjacent leg (A)<br />Opposite leg (O)<br />Hypotenuse (H)<br />Key Terms<br />H<br />O<br />ΞΈ<br />A<br />
    • 5. SOH: sin ΞΈ =π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’<br />CAH: cos ΞΈ =π΄π‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’<br />TOA: tan ΞΈ =π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’π΄π‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘<br />Β <br />SOH CAH TOA<br />
    • 6. sin 37Β° =<br />cos37Β° =<br />tan 37Β° =<br />SOH CAH TOA continued<br />21𝑓𝑑35𝑓𝑑<br />28𝑓𝑑35𝑓𝑑<br />21𝑓𝑑28𝑓𝑑<br />Β <br />35ft<br />21ft<br />37Β°<br />28ft<br />
    • 7. What is given?<br />Which trig function? <br />Finding the side length<br />12ft<br />sin 30Β° = 𝑋12𝑓𝑑<br />Β <br />X<br />sinΒ 30Β°1 = 𝑋12𝑓𝑑<br />Β <br />X= 6ft<br />30Β°<br />
    • 8. Using trig, find unknown<br />tan 20Β° = 𝑋6π‘š<br />Β <br />1<br />Β <br />X<br />X= 2.18m<br />20Β°<br />6m<br />X<br />cos 45Β° = 8𝑖𝑛π‘₯<br />Β <br />1<br />Β <br />45Β°<br />X= 11.31in<br />8in<br />
    • 9. What is known?<br /> tan ΞΈ = 34<br />Use π‘‘π‘Žπ‘›βˆ’1<br />π‘‘π‘Žπ‘›βˆ’1( 34 ) = ΞΈ<br />ΞΈ = 36.86Β°<br />Β <br />Using trig to find ΞΈ<br />3’<br />ΞΈ<br />4’<br />
    • 10. sin ΞΈ = 10π‘š15π‘š<br />π‘ π‘–π‘›βˆ’1(10π‘š15π‘šΒ ) = ΞΈ<br />ΞΈ = 41.81Β°<br />Β <br />Solve for ΞΈ<br />ΞΈ<br />15m<br />10m<br />cos ΞΈ = 7π‘π‘š9π‘π‘š<br />π‘π‘œπ‘ βˆ’1(7π‘π‘š9π‘π‘šΒ ) = ΞΈ<br />ΞΈ = 38.94Β°<br />Β <br />9cm<br />ΞΈ<br />7cm<br />
    • 11. Area of triangle<br />A = 𝐡𝐻2<br />A = 15βˆ—102 = 75π‘š2<br />Β <br />Finding the Area<br />10m<br />15m<br />
    • 12. What is given?<br />What is needed?<br />How is it found?<br />tan60 = 𝐡10<br />A =17.32π‘π‘šβˆ—10π‘π‘š2<br />Β <br />Finding area with trig<br />60Β°<br />10cm<br />B =17.32cm<br />=86.6π‘π‘š2<br />Β <br />
    • 13. Given<br />Needed<br />sin50 = 𝐻11<br />A= 13βˆ—8.432<br />Β <br />Non right triangles<br />H= 8.43in<br />11in<br />A=54.8𝑖𝑛2<br />Β <br />50Β°<br />13in<br />
    • 14. cos 60 = 𝐻22<br />Pythagorean theorem for the base<br />A= 19.05βˆ—112<br />Β <br />Find area of triangle<br />H=11in<br />60Β°<br />Β <br />22in<br />A=104.78𝑖𝑛2<br />Β <br />
    • 15. Given<br />Needed<br />B= X+Y<br />tan 45 = π‘₯16<br />tan 30 = 𝑦16<br />B=25.24cm<br />Β <br />Find area of triangle continued<br />Height = 16cm<br />16cm<br />45Β°<br />30Β°<br />X<br />Y<br />X=16cm<br />Y=9.24cm<br />A=16βˆ—25.242<br />Β <br />=201.92π‘π‘š2<br />Β <br />
    • 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 60Β° how long is the shadow?<br />Story Problems<br />tan 60 = 𝐿6<br />Β <br />L=10.39ft<br />60Β°<br />6ft<br />L<br />
    • 17. Story problems<br />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 52Β°. Will the ladder reach the window?<br />sin 52 = 𝐻40<br />H=31.52ft<br />Β <br />40ft<br />No, the ladder will not reach the window.<br />52Β°<br />
    • 18. SOH CAH TOA is key<br />Find the Given and Needed<br />Make own right triangle<br />Draw a picture<br />Wrap up<br />

    Γ—