Help struggling on this

Hello,

Let's assume CD=h, BD=x.

tan 24°=h/x ==>h=x*tan 24°

tan 16°=h/(7600+x)==>h=tan 16° *(7600+x)

==>x tan 24°=tan 16°*(7600+x)
==>x=(7600*tan 16°)/(tan 24°-tan 16°)

h=x*tan 24= (7600*tan 16°*tan 24°)/(tan 24°-tan16°)

b) CD=h=6122,2303...≈6122 (feet)

a) BC=h/sin 24°=15052,0746448...≈15052 (feet)

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