If the angle made by one of the ropes with the ground level is 30°, and height of
the pole is 8 m, then the length of the rope is
(a) 16v3 m (b) 16 m (c) 4 m (d) 8v3 m
3
The distance of the foot of the pole from the base of the second rope is 8 m. Its
angle of elevation from the ground is
(a) 30°
(b) 45"
(c) 60°
(d) Name of the above
The length of the second rope when first rope is 8 m long is
(a) 872 m (b) 8V3 m (c) 8 m (d) 8/3 m
If a rope is tied at an angle of 60°, then the ratio of the length of the rope to the
Tength of the pole is
(a) 1:13 (b) v3:1 (c) v3: 2
(d) 2:03
(vii)
If an artist takes 2 minutes to climb up the 8 m rope the speed of climbing is
(a) 1/15 m/sec (b) 15 m/s
(c) 4m/s (d) 6 mi's
Answers
Answer:
A. d) 8v3m
B. b) 45"
C. c) 8m
Answer:
the length of the rope is 4m.
the angle of elevation of the second rope from the ground is 45°
The length of the second rope will be 8√2 m.
Ratio of the length of the rope to the length of the pole is √3:2
Explanation:
let the pole be perpendicular of the triangle say AB
Let the ground be the base say BC
Let the first rope be the hypotenuse say AC
In triangle ABC,
sin 30°= perpendicular / hypotenuse
1/2 = 8/ hypotenuse
hypotenuse= 8/2
hypotenuse= 4 m
now, let the second rope be hypotenuse say AD
BD = 8m
In triangle ABD,
tan x = perpendicular / base
tan x = 8/8
tan x = 1
tan x = tan 45°. (tan 45°=1)
x = 45°
In the similar case when hypotenuse = AD
sin 45° = perpendicular / hypotenuse
1/√2 = 8/ hypotenuse
Hypotenuse = 8√2 m
Now, Length of the rope be hypotenuse
length of the pole be perpendicular
sin 60° = Perpendicular / hypotenuse
√3/2 = Perpendicular/ hypotenuse
Ratio = √3 : 2
Speed = Distance / Time
Speed = 8m / 120 sec
Speed = 1/15 m/ sec