1 / 13

Pre-Calculus

Pre-Calculus. Chapter 6 Additional Topics in Trigonometry. 6.2 The Law of Cosines. Objectives: Use Law of Cosines to solve oblique triangles (SSS or SAS). Use Law of Cosines to model & solve real-life problems. Use Heron’s Area Formula to find areas of triangles.

yoko-colon
Télécharger la présentation

Pre-Calculus

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. Pre-Calculus Chapter 6 Additional Topics in Trigonometry

  2. 6.2 The Law of Cosines Objectives: • Use Law of Cosines to solve oblique triangles (SSS or SAS). • Use Law of Cosines to model & solve real-life problems. • Use Heron’s Area Formula to find areas of triangles.

  3. Proof of Law of Cosines • Consider a triangle with threeacute angles. • The coordinates of the vertices are A(0, 0), B(c, 0), and C(x, y). • The altitude of the triangle is y. • We see that x= bcosAand y = b sin A.

  4. Proof continued…. • Side a is the distance from B to C.

  5. The Law of Cosines

  6. Example 1 • Find the angles of the triangle with sides a = 8 feet, b = 19 feet, and c = 14 feet. Hint: Find the largest angle first.

  7. Why Find the Largest Angle First? • What do we know about the cosine of an angle in QI? In QII? • In a triangle: • If cosθ > 0, then θ is ____________. • If cosθ < 0, then θ is ____________.

  8. Example 2 • Find the remaining angles and side of a triangle given A = 115°, b = 15 cm., and c = 10 cm.

  9. Example 3 • The pitcher’s mound on a women’s softball field is 43 feet from home plate. The distance between the bases is 60 feet. (The pitcher’s mound is not halfway between home plate and 2nd base.) How far is the pitcher’s mound from first base?

  10. Heron’s Area Formula • Given any triangle with sides of lengths a,b, and c, the area of the triangle is given by

  11. Example 5 • Find the area of a triangle having sides of lengths a = 43 m, b = 53 m, and c = 72 m.

  12. Formulas for Area of Triangle • Right Triangle: • Oblique Triangle: • Heron’s Formula (given all 3 sides):

  13. Homework 6.2 • Worksheet 6.2

More Related