Question

In ΔABC, AD ⊥ BC. BC = 100 cm, tan B = `2/3` and tan C = `6/11`. Find the length of AD.

Answer 1

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