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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.
Solution
(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).
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