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In triangle A B C ,A D is the altitude f...

In triangle `A B C ,A D` is the altitude from `Adot` If `b > c ,/_C=23^0,a n dA D=(a b c)/(b^2-c^2),` then `/_B=_____`

Text Solution

Verified by Experts

The correct Answer is:
`113^(@)`
In `DeltaADC, (AD)/(b)=sin 23^(@)`

` rArr AD=sin 23^(@)`
But `AD=(abc)/(a^(2)-c^(2)) " "` [ given]
`rArr (abc)/(b^(2)-c^(2))= b sin 23^(@)`
` rArr (a)/(b^(2)-c^(2))=(sin 23^(@))/(c)" ...(i)`
Again, in `DeltaABC`,
`(sinA)/(a)=(sin23^(@))/(c)`
`rArr (sinA)/(a)=(a)/(b^(-2)-c^(2))" "` [ from eq. (i)]
`rArr sin A=(a^(2))/(b^(2)-^(2))`
`rArr sin A=(k^(2) sin^(2) A)/(k^(2) sin ^(2)B-k^(2) sin^(2)C)`
`rArr sin A=(sin^(2)A)/(sin^(2)B-sin^(2)C)`
`rArr sin A=(sin^(2)A)/(sin (B+C) sin (B-C))`
`rArr sin A=(sin^(2)A)/(sin A*sin (B-C))`
`rArr sin (B-C)=1 " "[ :. sin A ne 0]`
`rArr sin (B-23^(@))=sin90^(@)`
`rArr B-23^(@) -90^(@)`
`B=113^(@)`
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