Question

Julio is visiting Bridal Veil Falls in Telluride Colorado. From the top of the 365 foot waterfall he looks down at an angle of depression of 27° and spots a bear fishing in the stream. To the nearest foot, how far is the bear from the base of the waterfall?

Answer 1

To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance. Using the given angle of depression of 27° and height of 365 feet, we can calculate that the bear is approximately 632 feet from the base of the waterfall.

Step-by-step explanation:

To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance.

In this case, we have an angle of depression of 27° and a height of 365 feet.

Let's denote the distance we're trying to find as x.

The tangent of the angle of depression is equal to the opposite side (365 feet) divided by the adjacent side (x).

So we can set up the equation tan(27°) = 365/x and solve for x.

Rearranging the equation, we have x = 365/tan(27°). Plugging in the values and using a calculator, we find that x is approximately 632 feet.

Answer 2

Step-by-step explanation:

The answer is 186.15 feet

First, we know that the height of the waterfall is 365 feet, we also know that the depression on which Julio looks down is 27 degrees. We could also assume that the angle at the base of the waterfall is 90 degrees for the sake of solving the equation. Since we are trying to find out the length of the base of the cliff and the Bear, we can use the tangent ratio since we already have an angle, a side adjacent to the angle, and a side opposite of the angle, which is what we are trying to solve for.

tan 27° = X/365

tan 27° = 0.510

0.510 = X/365

365*0.510 = 186.15

186.15 = X

*Note that the ratio for tangent which you use may vary, but as long as the answer remains close to 186 you should be fine*