Fsc Area Triangle Formulas
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Fsc Area Triangle Formulas as PDF for free.
More details
- Words: 479
- Pages: 1
mathcity.org Merging man and maths
Solution & Area of Oblique Triangle Textbook of Algebra and Trigonometry for Class XI
The Law of Cosine o a 2 = b2 + c 2 - 2bc cos a b2 + c 2 - a 2 o cos a = 2bc
Available online @ http://www.mathcity.org, Version: 2.0.1
o b 2 = c 2 + a 2 - 2ca cos b c2 + a 2 - b2 o cos b = 2ca
o c 2 = a 2 + b 2 - 2ab cos g a 2 + b2 - c 2 o cos g = 2ab
………………………………………………………………………………………………………………………………………
The Law of Sine a b c = = sin a sin b sin g
o
………………………………………………………………………………………………………………………………………
The Law of Tangent
( a -b ) ( )
a - b tan 2 o = a + b tan a + b 2
( b -g ) ( )
( g -a ) ( )
b - c tan 2 o = b + c tan b +g 2
c - a tan 2 o = c + a tan g +a 2
………………………………………………………………………………………………………………………………………
Half Angles Formulas o sin
a = 2
( s - b )( s - c ) bc
s(s - a) a = 2 bc a ( s - b )( s - c ) o tan = 2 s(s - a) o cos
where s =
o sin
b = 2
( s - c )( s - a )
o sin
ca
s ( s - b) b = 2 ca b ( s - c )( s - a ) o tan = 2 s ( s - b)
g = 2
( s - a )( s - b ) ab
s( s - c) g = 2 ab g ( s - a )( s - b ) o tan = 2 s(s - c)
o cos
o cos
a+b+c 2
………………………………………………………………………………………………………………………………………
Area of Triangle ( = D ) 1 1 1 o D = bc sin a = ca sin b = ab sin g 2 2 2 2 2 a sin b sin g b sin g sin a c 2 sin a sin b o D = = = = 2sin a 2sin b 2sin g s ( s - a )( s - b )( s - c )
o D =
(Hero’s Formula)
………………………………………………………………………………………………………………………………………
Circum Radius ( = R ) a b c o R = = = 2sin a 2sin b 2sin g
o R =
abc 4D
………………………………………………………………………………………………………………………………………
In Radius ( = r ) o r =
D s
………………………………………………………………………………………………………………………………………
Escribed Circle o r1 =
D s-a
o r2 =
D s -b
o r3 =
D s-c
……………………………………………………………………………………………………………………………………… Made By: Atiq ur Rehman
Email: [email protected]
h t t p :/ / ww w .mat h ci t y . org
Solution & Area of Oblique Triangle Textbook of Algebra and Trigonometry for Class XI
The Law of Cosine o a 2 = b2 + c 2 - 2bc cos a b2 + c 2 - a 2 o cos a = 2bc
Available online @ http://www.mathcity.org, Version: 2.0.1
o b 2 = c 2 + a 2 - 2ca cos b c2 + a 2 - b2 o cos b = 2ca
o c 2 = a 2 + b 2 - 2ab cos g a 2 + b2 - c 2 o cos g = 2ab
………………………………………………………………………………………………………………………………………
The Law of Sine a b c = = sin a sin b sin g
o
………………………………………………………………………………………………………………………………………
The Law of Tangent
( a -b ) ( )
a - b tan 2 o = a + b tan a + b 2
( b -g ) ( )
( g -a ) ( )
b - c tan 2 o = b + c tan b +g 2
c - a tan 2 o = c + a tan g +a 2
………………………………………………………………………………………………………………………………………
Half Angles Formulas o sin
a = 2
( s - b )( s - c ) bc
s(s - a) a = 2 bc a ( s - b )( s - c ) o tan = 2 s(s - a) o cos
where s =
o sin
b = 2
( s - c )( s - a )
o sin
ca
s ( s - b) b = 2 ca b ( s - c )( s - a ) o tan = 2 s ( s - b)
g = 2
( s - a )( s - b ) ab
s( s - c) g = 2 ab g ( s - a )( s - b ) o tan = 2 s(s - c)
o cos
o cos
a+b+c 2
………………………………………………………………………………………………………………………………………
Area of Triangle ( = D ) 1 1 1 o D = bc sin a = ca sin b = ab sin g 2 2 2 2 2 a sin b sin g b sin g sin a c 2 sin a sin b o D = = = = 2sin a 2sin b 2sin g s ( s - a )( s - b )( s - c )
o D =
(Hero’s Formula)
………………………………………………………………………………………………………………………………………
Circum Radius ( = R ) a b c o R = = = 2sin a 2sin b 2sin g
o R =
abc 4D
………………………………………………………………………………………………………………………………………
In Radius ( = r ) o r =
D s
………………………………………………………………………………………………………………………………………
Escribed Circle o r1 =
D s-a
o r2 =
D s -b
o r3 =
D s-c
……………………………………………………………………………………………………………………………………… Made By: Atiq ur Rehman
Email: [email protected]
h t t p :/ / ww w .mat h ci t y . org
Related Documents
Fsc Area Triangle Formulas
June 2020 7
Area Formulas
December 2019 10
Fsc Derivative Integration Formulas
June 2020 4
Fsc Trigonometric Formulas
June 2020 4
Formulas Area Superficie
June 2020 5