A surveyor made two sightings to the top of a mountain North of Santa Fe as shown in the picture to the right. Find the height o
f the mountain to the nearest foot.
1 answer:
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
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
You might be interested in