Answer:
CD ≈ 9.68 cm
Explanation:
use Pythagoras' identity in right triangle ABC to find BC
then use the sine ratio in right triangle BCD to find CD
BC² + AB² = AC² ( substitute values )
BC² + 3² = 8²
BC² + 9 = 64 ( subtract 9 from both sides )
BC² = 55 ( take square root of both sides )
=
, that is
BC =

using the sine ratio in Δ BCD
sin50° =
=
=
( multiply both sides by CD )
CD × sin50° =
( divide both sides by sin50° )
CD =
≈ 9.68 cm ( to 3 significant figures )