1 / 19

Chapter 5 Introduction to Trigonometry: 5.4 Modelling with Similar Triangles

Chapter 5 Introduction to Trigonometry: 5.4 Modelling with Similar Triangles. Humour Break. 5.4 Modelling with Similar Triangles. Goals for Today: Apply what we have learned about similar triangles to some word problems. 5.4 Modelling with Similar Triangles.

cheryl-vazquez
Download Presentation

Chapter 5 Introduction to Trigonometry: 5.4 Modelling with Similar Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 Introduction to Trigonometry: 5.4 Modelling with Similar Triangles

  2. Humour Break

  3. 5.4 Modelling with Similar Triangles Goals for Today: • Apply what we have learned about similar triangles to some word problems

  4. 5.4 Modelling with Similar Triangles • Ex. 1 – Rachel is standing beside a lighthouse on a sunny day. Rachel is 1.6m tall and the sun casts a shadow 4.8m long (on the ground). At the same time, the sun casts a shadow 75m long (on the ground). How tall is the lighthouse?

  5. 5.4 Modelling with Similar Triangles

  6. 5.4 Modelling with Similar Triangles

  7. 5.4 Modelling with Similar Triangles • AB is ll (parallel) to DE (same sun’s rays) • AC is on the same line as DF (both flat on ground) • ∠BAC = ∠EDF (same ∠) • ∠ACB = ∠DFE (both 90°) • ∠ABC = ∠DEF (180° ∆ rule) • Therefore, ∆ABC ~ ∆DEF

  8. 5.4 Modelling with Similar Triangles Since ∆ABC ~ ∆DEF • Plug in the known values • Cross-multiply • Simplify & solve for x

  9. 5.4 Modelling with Similar Triangles • Ex. 2 – A 3.6 m ladder is leaning against a wall with its base 2 m from the wall. A shorter 2.4 m ladder is placed against the wall parallel to the longer ladder. • (a) How far will the smaller ladder reach up the wall? • (b) How far will the smaller ladder’s base be from the wall?

  10. 5.4 Modelling with Similar Triangles

  11. 5.4 Modelling with Similar Triangles

  12. 5.4 Modelling with Similar Triangles • AB is ll (parallel) to DE (ladder at same ∠) • ∠ABC = ∠DEC (F pattern) • ∠BAC = ∠EDC (F pattern) • ∠ACB = ∠DCE (common 90°) • Therefore, ∆ABC ~ ∆DEC

  13. 5.4 Modelling with Similar Triangles • For (a), we first need to find out how far the larger ladder reaches up the wall using the pythagorean theorem…

  14. 5.4 Modelling with Similar Triangles • c² = a² + b² (Pytharorean theorem) • DE² = DC² + EC² (Substitute triangle sides) • 3.6² = DC² + 2² (Use algebra to solve) • 12.96 = DC² + 4 • 12.96 – 4 = DC² • DC²=8.96 (Take √ of both sides) • √DC²= √8.96 • DC≈3 m

  15. 5.4 Modelling with Similar Triangles

  16. 5.4 Modelling with Similar Triangles Since ∆ABC ~ ∆DEC (a) to find AC (how far smaller ladder reaches up the wall)… • Plug in the known values • Cross-multiply • Simplify & solve for AC

  17. 5.4 Modelling with Similar Triangles • How far will the smaller ladder be from the base of the wall? • Here, we have EC, so we can set-up a ratio using our similar triangle relationship

  18. 5.4 Modelling with Similar Triangles Since ∆ABC ~ ∆DEC to find BC (how far smaller ladder base will be from the wall)… • Plug in the known values • Cross-multiply • Simplify & solve for BC

  19. Homework • P.474, #1-4 & 6-13

More Related