Question

In triangle ABC, AB = 12 cm, LB = 58°, the perpendicular from A to BC meets it at D. The bisector of angle ABC meets AD at E. Calculate:
(i) The length of BD;
(ii) The length of ED.
Give your answers correct to one decimal place.

Answer 1

(i) In right-angled Δ ABD,

`"BD"/"BA" = cos 58°`

BD = BA cos 58°

= 12 x (0.5299) cm
= 6.3588 cm
(ii) In right-angled Δ EBD,

`"ED"/"BD" = tan 29°`

ED = BD tan 29°

= (6.3588)(0.5543) cm
= 3.52 cm (approx).