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sines of angle of triangle are ratio 4:5:6 proof the cosine of the angles are 12:9:2
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Answer 1

✌♥✌hey mate here is your answer ✌♥✌

♒given in triangle ABC

♒sinA:sinB:sinC=4:5:6

♒to prove.......

♒cosA:cosB:cosC=12:9:2

♒according to sine law ratio of side is same in ratio as the ratio of angle

♒now let us consider a triangle with side 4,5,6

♒now as we know that,

♒cosA=b²+c²-a²/2bc

=(5)²+(6)²-(4)²/2(5)(6)

=45/60

=12/16

♒now cosB=(6)²+(4)²-(5)²/2(6)(4)

=9/16

♒cosC=(5)²+(4)²-(6)²/2(5)(4)

=2/16

♒so

♒cosA:cosB:cosC=12/16:9/16:2/16

♒cosA:cosB:cosC=12:9:2

♒hence proved

♥⛄hope it will help you ⛄♥

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