A rope dancer was walking on a loose rope tied to the tops of two equal post of height 9m. when he was 2.7m above the ground ,it was found that the stretched parts of the other rope made angles of 30 and 60.Find the length of the rope,with figure
assuming you meant that the rope made those angles with the poles, then look at the figure, and you can see that the two parts of the rope had lengths
(90-2.7) / cosθ
where θ is 30° or 60°
no idea where the "other rope" is ...