Question

Trigonometry Question, check pic.

Answer 1

`\text{AD is a bisector of angle BAC, so}\\\\\angle DAC = \angle BAD = 17^(\circ)~ \text{and}~ \angle BAC = 17^(\circ) + 17^(\circ)=34^(\circ)\\\\\text{In}~ \triangle ADB\\\\~~~~~~~\tan \angle BAD = (DB)/(AB)\\\\\implies DB = AB\tan \angle BAD \\\\~~~~~~~~~~~~=21 \tan 17^(\circ)\\\\`

`\text{In}~ \triangle ABC\\\\~~~~~~~\tan \angle BAC = (CB)/(AB)\\\\\implies BC = AB \tan \angle BAC\\\\\implies DB+CD = AB\tan \angle BAC\\\\\implies CD = AB \tan \angle BAC - DB\\\\\implies CD=21\tan 34^(\circ)-21 \tan 17^(\circ)\\\\\implies x\approx8 ~ \text{cm}`