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प्रश्न
In ΔABC, AD ⊥ BC. BC = 100 cm, tan B = `2/3` and tan C = `6/11`. Find the length of AD.
बेरीज
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उत्तर
Given
BC = 100cm
AD ⊥ BC
tan B = `2/3, tan C = 6/11`
△ABD and △ACD
tan B = `(AD)/(BD)`
= BD = `(AD)/(tan B)`
= tan C = `(AD)/(DC)`
= DC = `(AD)/(tanC)`
Since BC = BD + DC
`(AD)/(tanB) + (AD)/(tan C) = 100`
`AD(1/tan B + 1/tan C) = 100` ...[Plug the values]
`AD(3/2 + 11/6) = 100`
`AD(10/3) = 100`
`AD = 100 ⋅ 3/10`
AD = 30 cm
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