Question

A blimp is providing aerial views of a football game. The television camera sights the stadium at a 7° angle of depression. The blimp's altitude is 400 m. What is the line-of-sight distance from the blimp to the stadium?

Question 13 options:

5144.7 meters


4107.8 meters


3282.2 meters


2970.6 meters

Answer 1

To calculate the line-of-sight distance from the blimp to the stadium, we can use trigonometry. Given that the altitude of the blimp is 400 m and the angle of depression is 7°, we can visualize this situation as a right triangle where:

- The height (opposite side) is 400 m.
- The angle of depression from the blimp to the stadium is 7°.
- The line-of-sight distance is the hypotenuse of the triangle.

Using the sine function, we have:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Here, we denote the line-of-sight distance (hypotenuse) as \( d \). The equation becomes:

\[
\sin(7°) = \frac{400}{d}
\]

Rearranging this for \( d \):

\[
d = \frac{400}{\sin(7°)}
\]

Now, we will compute the value of \( \sin(7°) \):

\(\sin(7°) \approx 0.121869\)

Now we substitute this back into the equation:

\[
d = \frac{400}{0.121869} \approx 3282.2 \text{ meters}
\]

Thus, the line-of-sight distance from the blimp to the stadium is approximately **3282.2 meters**.

The correct answer is:

**3282.2 meters**