Malfatti: Trig supplement

The following trigonometric expression arises in Malfiatti's problem [math]\;\;\; \sin² λ = \sin² α + \sin² β+ 2 \sinα \sinβ \cosλ [/math] What is not obvious, is this: if the equality holds, then [i]α+β = λ[/i]. And we may draw λ as the external angle of a triangle, with opposite internal angles α, β. ______________ [b]Malfatti's Problem:[/b] 1. Describe the constraints: [url]http://www.geogebratube.org/material/show/id/32079[/url] 2. Solution [url]http://www.geogebratube.org/material/show/id/32233[/url] [b]→3. Trig Supplement[/b] This is problem # 30 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics.[/i] More: (http://www.geogebratube.org/material/show/id/73813)

 

Ryan Hirst

 
نوع منبع آموزشی
کاربرگ
برچسب‌ها
angle  sum  trigonometry 
سن گروه مخاطب
19+
زبان
English (United States)
 
 
نسخه جئوجبرا
4.4
مشاهده‌ها
4736
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