Question

Omar and Mackenzie want to build a pulley system by attaching one end of a rope to their 8-foot-tall tree house and anchoring the other end to the ground 28 feet away from the base of the treehouse. How long, to the nearest foot, does the piece of rope need to be?

a. 26ft
b. 27ft
c. 28ft
d. 29ft

Answer 1

d. 29ft

Explanation:

Using pythagoras theorem which states that

a^2 + b^2 = c^2

where a and b are the opposite and adjacent sides of a right angled triangle and c is the hypotenuse side

From the attached image, Let the length of the rope be x

`x^(2) = 8^(2)+ 28^(2) \\`

`x^(2) = 64 + 784`

`x^(2) = 848`

`x =√(848)`

`x = 29.12`

x≈29