if a:b:c=7:8:9 find cosA:cosB:cosC
Answers
Answer:
sinA : sinB : sinC = 7 : 8 : 9 ( sine Rule)
sin ^2 A : sin ^2 B : sin ^2 C = 49 : 64 :81
( 1 - ( cos A) ^2 ) : ( 1 - ( cos B) ^2 ) : ( 1 - ( cos C) ^2 ) = 49 : 64 : 81
- ( cos A) ^2 ) : - ( cos B) ^2 : - ( cos C) ^2 = 48 : 63 : 80
( cos A) ^2 : ( cos B) ^2 : ( cos C) ^2 = 48 : 63 : 80
cos A : cos B : cos C = √48 : √63 : √80
cos A : cos B : cos C = √16* 3 : √7 * 9 : √16 * 5
cos A : cos B : cos C = 4√3 : 3√7 : 4√5.
Solution : cos A : cos B : cos C = 4√3 : 3√7 : 4√5.
answered Mar 29, 2014 by friend Mentor
0
votes
Let a = 7x, b = 8x , c = 9x
cos(A) = (b2 + c2 - a2)/2bc
= [(8x)2 + (9x)2 - (7x)2 ]/2(8x)(9x)
= (64x2 + 81x2 - 49x2 )/144x2
= x2 (64 + 81 - 49 )/144x2
= 96/144
= 2/3
cos(B) = (a2 + c2 - b2)/2ac
= [(7x)2 + (9x)2 - (8x)2 ]/2(7x)(9x)
= (49x2 + 81x2 - 64x2 )/126x2
= x2 (49 + 81 - 64 )/126x2
= 66/126
= 11/21
cos(C) = (a2 + b2 - c2)/2ab
= [(7x)2 + (8x)2 - (9x)2 ]/2(7x)(8x)
= (49x2 + 64x2 - 81x2 )/112x2
= x2 (49 + 64 - 81 )/112x2
= 32/112
= 2/7
The three fractions are 2/3 ,11/21, 2/7
Write the above fractions with same denominator.
14/21, 11/21, 6/21
cos(A) : cos(B) : cos(C) = 14 : 11: 6
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