Astudent measures the angle of elevation of a cloud to be 65° at point a. then the student moves 100 feet in the direction of the cloud and takes a second observation at point b. at point b the elevation is 75. using this information find the height, to the nearest foot, of the cloud directly above the ground.

See the attached figure to better understand the problem

we know that 
in the triangle ACD

tan 65°=CD/(100+x)------> CD=(100+x)*tan 65°------> equation 1

in the triangle BCD

tan 75°=CD/x---------> CD=x*tan 75°------> equation 2

equals 1 and 2
(100+x)*tan 65°=x*tan 75°-----> (100+x)*2.14=x*3.73
100*tan 65+x*tan 65=x*tan 75-----> x*{tan 75-tan 65]=100* tan 65
x=100* tan 65/[tan 75- tan 65]------> x=135.08 ft

CD=x*tan 75°------->CD=135.08*tan 75°------> CD=504.12 ft

the answer is
the height of the cloud directly above the ground is 504 ft