Question

A blimp hovers 400 feet above a stadium. A fan is standing outside the stadium. To directly view the blimp, the fan looks up at an angle of elevation of 7 degrees (from the ground). Rounded to the nearest foot, how far away from the stadium is the fan standing SHOW WORK

Answer 1

To solve the problem, we can use trigonometry, specifically the tangent function. The situation can be modeled as a right triangle where:

- The height of the blimp (opposite side) = 400 feet
- The distance from the fan to the stadium (adjacent side) = \(d\) feet
- The angle of elevation = 7 degrees

The relationship between the angle, the opposite side, and the adjacent side is given by the tangent function:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In our case, we have:

\[
\tan(7^\circ) = \frac{400}{d}
\]

We can rearrange this equation to solve for \(d\):

\[
d = \frac{400}{\tan(7^\circ)}
\]

Now, we can calculate \(\tan(7^\circ)\). Using a calculator:

\[
\tan(7^\circ) \approx 0.122784
\]

Now substituting this back into the equation for \(d\):

\[
d \approx \frac{400}{0.122784}
\]

Calculating the value:

\[
d \approx 3255.72
\]

Rounding this to the nearest foot, we find:

\[
d \approx 3256 \text{ feet}
\]

Thus, the fan is standing approximately **3256 feet** away from the stadium.