A woman standing on a hill sees a flagpole that she knows is 30 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.)
I need help getting started i don't know where to begin.
I need help getting started i don't know where to begin.
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Looking at the flagpole if one angle is elevation and the other depression then you can draw a perpendicular line to the woman from the flagpole.
The angle above the horizontal is ( 18° ) and the angle below the horizontal is ( 14°)
both add to 32 °
Since the perpendicular has an angle of 90° to the pole the above triangle has the interior angles 18° 90° and 72°
the lower triangle has the interior angles 14° 90° and 76°
now for the whole triangle 32°+72°+76° = 180 °
Now use the law of sines to fine the lengths
a / sin A = ,b/Sin B = c/ sin C
let a = 30 angle A = 32° Let angle B = 76° Let angle C=72°
b/sin 76° = 30/ sin 32° thus b= 54.93 ft ( distance to top of pole)
c/ sin 72° = 30 / sin 32° thus c = 53.84ft ( distance to bottom of pole)
Cos( Θ ) = adj / hyp then hyp * cos(Θ) = adj
54.93 cos(18°) = appros 52. ft ( perpendicular to pole)
53.84 cos (14) = approx. 52 ft
The angle above the horizontal is ( 18° ) and the angle below the horizontal is ( 14°)
both add to 32 °
Since the perpendicular has an angle of 90° to the pole the above triangle has the interior angles 18° 90° and 72°
the lower triangle has the interior angles 14° 90° and 76°
now for the whole triangle 32°+72°+76° = 180 °
Now use the law of sines to fine the lengths
a / sin A = ,b/Sin B = c/ sin C
let a = 30 angle A = 32° Let angle B = 76° Let angle C=72°
b/sin 76° = 30/ sin 32° thus b= 54.93 ft ( distance to top of pole)
c/ sin 72° = 30 / sin 32° thus c = 53.84ft ( distance to bottom of pole)
Cos( Θ ) = adj / hyp then hyp * cos(Θ) = adj
54.93 cos(18°) = appros 52. ft ( perpendicular to pole)
53.84 cos (14) = approx. 52 ft