Question

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​

Answer 1

Answer:

A. d) 8v3m

B. b) 45"

C. c) 8m

Answer 2

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