Question

Robin Hood wants to measure the length of a rope his merry men have recently detached from deputy sheriff. Robins stands on a cliff and shoots an arrow with the rope attached at a hamburger on the plain below little John paces 30 yards from the foot of the cliff to the hamburger and measures 45° between the taut cord and the ground

How long is the cord

Answer 1

The cord is 42.42 yards long

Step-by-step 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

`cos45\°=adjacent side/hypotenuse\\1/√(2) =30/hypotenuse\\=hypotenuse=30*√(2\\) =42.42 yards`

The length of the rope is 42.42 yards.