SOLUTION: A woman is standing on a hill looking at a flag pole known to be 36 feet tall. If she measures 18◦ angle to the top of
the flag pole and a 14◦ angle to the bottom of t
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Question 469718: A woman is standing on a hill looking at a flag pole known to be 36 feet tall. If she measures 18◦ angle to the top of
the flag pole and a 14◦ angle to the bottom of the flag pole as shown, how far away is she standing from the flag pole?
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
Draw 3 lines from the woman to the flag pole , one to the top, one to the bottom and one straight across perpendicular to flag pole.
This forms 2 right triangles.
Angle opposite flag pole in top triangle is 18 degrees
Angle opposite flag pole in bottom triangle is 14 degrees
The adjacent side for both angles is the distance from the flag pole, call it d.
Let the length of the top part of flag pole be x, then length of bottom part is 36-x.
In this way their sum equals 36, the length of the flag pole.
Use trig relationships to solve for d
Note that tan(theta) = opp/adj
Thus
Solve for x in 1st equation:
Substitute this in for x in 2nd equation
Solve for d:
Multiply by d on both sides
Add d*tan(18) on both sides
Factor d from left side
Divide by tan(14)+tan(18) on both sides
Using scientific calculator
Therefore the woman is approximately 62.7 ft away from the flag pole.
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