From the >me a small airplane is
240 feet high and 5200 ground feet
from its landing runway, the plane
descends in a straight line to the
runway. Determine the plane’s
angle of decent. Round to the
nearest hundredth.

To determine the plane's angle of descent, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle to the opposite and adjacent sides of a right triangle.

- The opposite side is the height of the plane: 240 feet.
- The adjacent side is the distance to the runway along the ground: 5200 feet.

We can set up the equation:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{240}{5200}
\]

Now, solve for the angle \(\theta\) by taking the inverse tangent (\(\tan^{-1}\)) of both sides:

\[
\theta = \tan^{-1}\left(\frac{240}{5200}\right)
\]

Let's calculate this.The plane's angle of descent is approximately \( 2.64^\circ \), rounded to the nearest hundredth.

Would you like more details on this calculation, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How does the angle of descent change if the ground distance decreases?
2. What would happen to the angle if the plane were higher but the ground distance remained the same?
3. Can the angle of descent be more than 45 degrees for typical airplanes?
4. How would you calculate the time it takes for the plane to land if its speed is known?
5. What other trigonometric functions could help determine descent-related problems?

**Tip:** When dealing with angles and right triangles, the tangent function is particularly useful for relating height and horizontal distance.

From the >me a small airplane is 240 feet high and 5200 ground feet from its landing runway, the plane descends in a straight line to the runway. Determine the plane’s angle of descent. Round to the nearest hundredth.

Learn how to calculate the angle of descent for an airplane that is 240 feet high and 5200 feet away from the runway. This problem uses trigonometric principles, including the tangent function and inverse tangent, to determine the angle of descent. Suitable for students in Grades 9-12.

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