Question

Find the length of AD. Given: ∠ABC = 60°, ∠DBC = 45° and BC = 24 cm.

Answer 1

In ΔABC,

tan60° = `"AC"/"BC"`

⇒ `sqrt(3) = "AC"/(24)`
⇒ AC = `24sqrt(3)"cm"`
In ΔDBC,

tan45° = `"DC"/"BC"`

⇒ 1 = `"DC"/(24)`
⇒ DC = 24cm
Now,
AC = AD + DC
⇒ AD 
= AC - DC
= `24sqrt(3) - 24`
= `24(sqrt(3) - 1)"cm"`.