From a point on the floor the angle of elevation to the top of a door is 47 degreees, while the angle of elevation to the ceiling above the door is 59 degrees. If the ceiling is 10 feet above the floor, what is the vertical dimension of the door?
2007-08-30 08:41:49 · 5 answers · asked by L J 3 in Science & Mathematics ➔ Mathematics
D = distance from point to the door
tan(58) = 10/D
D = 10/tan(59)
H = height of door
tan(47) = H/D = Htan(59)/10
H = 10 tan(47)/tan(59)
H = 6.44 feet
2007-08-30 09:05:30 · answer #1 · answered by Captain Mephisto 7 · 0⤊ 0⤋
Let ceiling height is H, door height is h and horizontal distance to the door L. Then tan(47)=h/L while tan(59)=H/L. Then L=H/tan(59) and h=tan(47)*L=H*tan(47)/tan(59)
2007-08-30 16:05:55 · answer #2 · answered by Alexey V 5 · 0⤊ 0⤋
let the distance of the point from the door be x;
10/x=tan 59,
h/x=tan 47, h= vertical dimension of the door.
h=x tan 47
=10x tan47/tan59
=10x1.0724/1.6643
=6.4435ft ANS.
2007-08-30 16:29:18 · answer #3 · answered by Anonymous · 0⤊ 0⤋
tan(59 deg) = 10 /x, where x = horizontal distance to door/ceiling
x = 6.0086
tan (47 deg) = y / 6.0086 ; where y= vertical height of door
y= 6.4434 feet
2007-08-30 16:10:54 · answer #4 · answered by Mikeeeey 2 · 0⤊ 0⤋
sine(59)=.857167=10/L
L=10/.857167=11.66633=distance to door
sine(47)=.731354=height/distance=H/L
H=.731354*11.66633
Door Height = 8.532217
2007-08-30 16:02:27 · answer #5 · answered by Flyer 4 · 0⤊ 0⤋