Question

A circus artist is climbing a rope, which is tightly stretched and tied
from the top of a vertical pole of height 18 m to the ground. Find the
length of the rope, if the angle made by the rope with the ground
level is 30°
​

Answer 1

Step-by-step explanation:

let the height of the pole be AB

assuming that rope is tied at point C

it is given that ,

length of rope = 18m

hence , AC = 18m

also angle made by rope with the ground level = 30°

we need to find height of pole i.e AB

since the pole is vertical ,

/_ ABC = 90°

in right triangle ABC

$sin \: c \: = \frac{side \: opposite \: to \: angle \: c}{hypotenuse} \\ sin \: 30 \: degree \: = \frac{ab}{ac } \\ \frac{1}{2 } = \frac{ab}{18} \\ \frac{1}{2} \times 18 = ab \\ 9 = ab \\ ab = 9 \\ height \: of \: pole \: = ab = 9$