Answer:
681 feet
Step-by-step explanation:
Let x represent the distance between campsite and the base of the cliff.
We have been given that Haylee hikes to the top of a 120-foot vertical cliff. From the top of the cliff, the angle of depression to her campsite is 10∘. We are asked to find the distance between campsite and the base of the cliff.
We can see that angle of depression forms a right triangle with respect to ground, cliff and campsite.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(10^{\circ})=\frac{120}{x}[/tex]
[tex]x=\frac{120}{\text{tan}(10^{\circ})}[/tex]
[tex]x=\frac{120}{0.176326980708}[/tex]
[tex]x=680.5538183559[/tex]
Upon rounding to nearest foot, we will get:
[tex]x\approx 681[/tex]
Therefore, the campsite is 681 feet away from the base of the cliff.
