Question

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∘. How far away from the campsite is the base of the cliff? Round to the nearest foot.

Answer 1

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.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(10^{\circ})=\frac{120}{x}$

$x=\frac{120}{\text{tan}(10^{\circ})}$

$x=\frac{120}{0.176326980708}$

$x=680.5538183559$

Upon rounding to nearest foot, we will get:

$x\approx 681$

Therefore, the campsite is 681 feet away from the base of the cliff.