Question

madison is on the top of an 80 foot building. she is creating a zipline course to the ground with 100 feet of cable. how far from the base of the building will she need to anchor the cable to make the zipline cable tight? 20 feet 60 feet 180 feet

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the base of the building be \(x\). The building height \(a = 80\) feet (one leg of the right - triangle), the cable length \(c=100\) feet (hypotenuse of the right - triangle). According to the Pythagorean theorem \(a^{2}+x^{2}=c^{2}\), so \(x^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 80\) and \(c = 100\) into the formula: \(x^{2}=100^{2}-80^{2}\).

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Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{3600}=60\)

Answer:

60 feet