SOLUTION: The angle of elevation of the top of a flagpole from a point on level is 30°. From another point on the ground 20m nearer the flagpole, the angle of elevation is 60°. Calculate t

Algebra ->  Test -> SOLUTION: The angle of elevation of the top of a flagpole from a point on level is 30°. From another point on the ground 20m nearer the flagpole, the angle of elevation is 60°. Calculate t      Log On


   

Question 1205424: The angle of elevation of the top of a flagpole from a point on level is 30°. From another point on the ground 20m nearer the flagpole, the angle of elevation is 60°. Calculate the height of the flagpole.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

h is the flagpole
a is 20m
b is unknown distance along level ground to flagpole, from where 60 degree measure is taken
...
We have:
+tan%2830%29+=+h%2F%28a%2Bb%29+=+h%2F%2820%2Bb%29+ and
+tan%2860%29+=+h%2Fb+
Solving each of these for h:
+h+=+%2820%2Bb%29tan%2830%29+ and +h+=+b%2Atan%2860%29+

Solve for b by setting the above two equation equal:
+++%2820%2Bb%29%2Atan%2830%29+=+b%2Atan%2860%29+
+++%2820%2Bb%29%28sqrt%283%29%2F3%29+=+b%2Asqrt%283%29+
...
++b+=+10m+

Then from +h+=+b%2Atan%2830%29+: +h+=+10%2Asqrt%283%29+ or approx +highlight%28+17.32m%29+ to two decimal places
======
a = 20m from "...another point on the ground 20m nearer the flagpole,"
======


Dear student, please read the entire problem statement carefully!

In the diagram below, I have added points "A" and "B" which are the two points where the angles are measured.   If you start at "A" and walk to "B" (which is distance 'a'), you will have walked 20m.   Point "B" is "20m nearer to the flagpole."  This is stated clearly within the original problem statement.