Question

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I have question
solve for me
sines of angle of triangle are ratio 4:5:6 proof the cosines of the angles are 12:9:2
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Answer 1

The sines of the angles of a triangle are in ratio 4:5:6. Find the ratio of their cosines
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From the Sine Law, the ratio of the sides is also 4:5:6
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Use a triangle with sides of 4, 5 & 6:
cos(A) = 3/4
cos(B) = 9/16
cos(C) = 1/8
--> 12:9:2

Answer 2

✌♥✌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 ⛄♥

✌✌✌mark me brainliest ✌✌✌