Question

1. In triangle ABC, AD = 12 cm, angle B = 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

Answer:

(i) In right angled ABD,

BD/BA = cos 58˚

BD = BA cos 58˚

= 12 × (0.5299) cm

= 6.3588 cm

(ii) In right angled EBD,

ED/BD = tan 29˚

ED = BD tan 29˚

= (6.3588)(0.5543) cm

= 3.52 cm.(approx.)

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