The cord is 42.42 yards long
Explanation:
Robin stands on a cliff and shoots an arrow that has a rope attached to it. Little John paces 30 yards from the foot of the cliff and measures the angle between the taut rope and ground to be 45°.
The length of the rope can be determined using trigonometry.
The cliff, taut rope and the ground forms a right angled triangle with the rope as the hypotenuse, ground as the base and cliff as the height.
The angle between base and hypotenuse is 45°.
length of base=30 yards
[tex]cos45\°=adjacent side/hypotenuse\\1/\sqrt{2} =30/hypotenuse\\=hypotenuse=30\times\sqrt{2\\} =42.42 yards[/tex]
The length of the rope is 42.42 yards.
