If twenty-four is subtracted from a number, the result is the same as the number divided by nine. what is the number?

X - 24  = x /9
multiply through by 9:-
9x - 216 = x
8x = 216 
x = 27 answer

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)

=