Asurveyor made two sightings to the top of a mountain north of santa fe as shown in the picture to the right. find the height of the mountain to the nearest foot.

See the attached figure to better understand the problem

in the triangle ABD
tan 29=BD/(525+x)------> BD=(525+x)*tan 29------> equation 1

in the triangle CBD
tan 38=BD/x-------> BD=x*tan 38-----------> equation 2

equals 1 and 2

(525+x)*tan 29=x*tan 38----> 525*tan29+x*tan29=x*tan38
x*[tan38-tan29]=525*tan29---> x=525*tan29/[tan38-tan29]---> x=1282.12 ft

BD=x*tan 38-----> 1282.12*tan38-----> BD=1001.71 ft-----> 1002 ft

the answer is
1002 ft