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Question

# A zip line is constructed across a valley, as shown in the diagram. What is the width w of the valley?

Solution

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We are given a SAS triangle so we solve for $w$ using the Law of Cosines:

$w^2=25^2+84^2-2(25)(84)\cos 102\text{\textdegree}$

$w=\sqrt{25^2+84^2-2(25)(84)\cos 102\text{\textdegree}}$

$w=\sqrt{7681-4200\cos 102\text{\textdegree}}$

Use a calculator in DEGREE mode:

$\color{#c34632}w\approx 92.5\text{ ft}\color{white}\tag{1}$

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