Question

Tessa wants to install a zipline between two trees. The zipline will be strung between the trees at points 42 feet and 3 feet high. Suppose the trees are 60 feet apart. What is the length of the zipline to the nearest tenth of a foot

Answer 1

The length of the zipline is found using Pythagoras's theorem, which gives

the length of the hypotenuse side of a right triangle.

• Length of the zipline is approximately 71.56 feet

Reasons:

Height at which the zipline will be tied to one of the trees = 42 feet

Height at which the zipline will be tied to the other tree = 3 feet

The distance between the trees = 60 feet

Required:

The length of the zipline

Solution:

The length of the zipline is found as follows;

Taking one of the trees to be at the origin, the coordinates of one of the tying point = (0, 42)

The coordinates of the other tying point = (60, 3)

The in the imagined right triangle formed by the zipline and the distance

between the trees, the length of the zipline is given by Pythagoras theorem

as follows;

Length of zipline = $\sqrt{(60 - 0)^2 + (3 - 42)^2} = 3 \cdot \sqrt{569}$ ≈ 71.56

Length of the zipline ≈ 71.56 ft.

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