trig
posted by Dominic .
A woman standing on a hill sees a flagpole that she knows is 65 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. Find her distance x from the pole. (Round your answer to one decimal place.)

Draw the woman on the hill with her line of sight touching the pole somewhere in the middle.
label her line of sight x, the top part of the pole h and the bottom part of the pole 65h
You now have 2 rightangled triangles
for the top one:
tan18° = h/x
h = xtan18
for the bottom part:
tan14 = (65h)/x
xtan14 = 65h
h = 65  xtan14
then xtan18 = 65  xtan14
xtan18  xtan14 = 65
x(tan18tan14) = 65
x = 65/(tan18+tan14) = 113.2
Respond to this Question
Similar Questions

MATH TRIG
FROM A DISTANCE OF 80 M. THE ANGLE OF ELEVATION OF THE TOP OF A FLAGPOLE IS 18 DEGREES. dETERMINE THE HEIGHT OF THE FLAGPOLE.(NEAREST TETH OF A M. mY CONFUSION IS ANGLE OF DEPRESSION AND ANGLE OF ELEVATION. mY TECHER CALLS FROM TOP … 
Precalculus
A woman standing on a hill sees a flagpole that she knows to be 60 ft tall. the angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. find her horizontal distance … 
Precalculus
A woman standing on a hill sees a flagpole that she knows to be 60 ft tall. the angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. find her horizontal distance … 
math
a flagpole is 25 feet tall. a truck runs into the pole and bends it at the very bottom of the pole but the rest of the pole remains straight. after the accident we measure the angle of elevation to the top of the pole from a point … 
Trig
A 60foot flagpole stands on top of a building. From a point on the ground the angle of elevation to the top of the pole is 45 degrees and the angle of elevation to the bottom of the pole is 42 degrees. How high is the building? 
Trig
A vertical pole stands on a 20° slope from 50 m down the slope from the pole the angle of elevation of the top of the pole is 35 degrees. How tall is the pole 
Trigonometric
A woman standing on a hill sees a flagpole that she knows is 55 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. Find her distance x from the pole. 
Math
From the top of an 8m house the angle of elevation to the top of the schools flagpole across the street is 9 degrees The angle of depression is 42degrees to the bottom of the pole How tall is the flagpole 
Trigonometry
10. A person notices that the angle of elevation from where he is standing to the top of a pole is 40°. Then he backs up 12 feet and notices that the angle of elevation to the top of the pole is now 32°. How tall is the pole? 
maths
from a point P on a level ground and directly west of a pole,the angle of elevation from the top of the pole is 045 and from point Q east of the pole the angle of elevation of the pole the angle of elevation of the top of the pole …