A flagpole is situated at the top of a building 120 ft tall from a point in the same horizontal plane as the base of the building, the angles of elevation of the top and bottom of the flagpole are 73.2 degrees and 67.2 degrees. Respectively how tall is the flagpole?
2007-10-26 01:40:05 · 5 answers · asked by delixir_21 1 in Science & Mathematics ➔ Mathematics
Let:-
d ft = horizontal distance from bottom of building
h ft = height of tower
tan 67.2 = 120/d
d = 120 / tan 67.2
tan 73.2 = (120 + h) / d
d = (120 + h) / tan 73.2
120 / tan 67.2 = (120 + h) / tan 73.2
120 tan 73.2 = tan 67.2 (120 + h)
397.5 = 285.5 + 2.38 h
2.38 h = 112
h = 47.1
Flagpole is 47.1 ft
2007-10-29 22:53:07 · answer #1 · answered by Como 7 · 1⤊ 0⤋
This sounds like we need to work with TANGENTS :)
First of all; tan(67.2) = 120/x where x is the horizontal distance to the point where we are measuring from.
x = 120/tan(67.2)
x = 50.44
Secondly, we have tan(73.2) = y / x
where y is the height of the top of the flagpole.
y = x * tan(73.2)
y = 167.076
Now this is the height that the top of the flagpole is above the ground, so the flagpole it self is 167.076 - 120 or 47.076 feet tall.
2007-10-26 01:55:26 · answer #2 · answered by PeterT 5 · 1⤊ 0⤋
As measured from the ground the angle of elevation of the bottom of the pole, will tell you how far the viewer is from the base of the building, x.
tan 67.2 = 120/x
x = 120/tan 67.2
x = 50.44 ft
use that to find the elevation to the top of the pole, y
tan 73.2 = y/50.44
50.44 tan 73.44 = y
y = 167 ft
from that subtract the height of the building to get the height of the flag pole.
47 ft
2007-10-26 02:00:19 · answer #3 · answered by Peter m 5 · 0⤊ 0⤋
This one i think of you are going to be able to desire to draw it out to remedy it out, it's going to be much less confusing. you could remedy this by employing employing perspective of melancholy or elevation. i visit persist with perspective of elevation. So if perspective of melancholy for nearest milestone A is 22?, then perspective of elevation from A to balloon would be = ninety? - 22? = sixty 8? further perspective of elevation from farthest milestone B = ninety? - 20? = 70? And we can use here variables h = vertical top of the balloon from the floor x = horizontal distance between balloon and A y = horizontal distance between balloon and B h and x form 2 fringe of a suggestions-blowing triangle between A and balloon x = h tan sixty 8? h and y form 2 fringe of a suggestions-blowing triangle between B and balloon y = h tan 70? Subtracting the final 2 equations y - x = h tan 70? - h tan sixty 8? considering y and x are milestones; so as that they seem to be one million mile aside y - x = one million (h tan 70? - h tan sixty 8?) = one million h = one million/ (tan 70? - tan sixty 8?) = one million / (2.747 - 2.475) h = one million / 0.272 = 3.676 miles
2017-01-04 11:20:18 · answer #4 · answered by Anonymous · 0⤊ 0⤋
+ A
Flag pole
+D
120 ft tall bldg
+.....67.2 Deg+ 73.2 Deg to top point (A)
B...................C
BC/120= cot 67.2
BC = 120*cot (67.2 degree) = 50.4433 ft
how tall is flag pole?
50.4433*{(tan 73.2)-(tan 67.2)}= pole length = 47.0764 ft
2007-10-26 03:25:03 · answer #5 · answered by kkr 3 · 0⤊ 1⤋