Question

Find the length of AD.
Given: ∠ABC = 60^o.
∠DBC = 45^o
and BC = 40 cm.

 

Answer 1

From right triangle ABC,

tan 60° = `"AC"/"BC"`

⇒ `sqrt(3) = "AC"/40`

⇒ AC = `40sqrt(3)"cm"`

From right triangle BDC,

tan 45° = `"DC"/"BC"`

⇒ 1 = `"DC"/(40)`

⇒ DC = 40 cm

From the figure, it is clear that AD = AC - DC

⇒ AD = `40sqrt(3) - 40`

⇒ AD = `40(sqrt3 - 1)`

⇒ AD = 29.28 cm