This image represents a right triangle, where:

• The distance between the airplane and the airport (hypotenuse) is 290 meters.
• The horizontal distance from the airplane's current position to the airport (adjacent side) is 210 meters.

To find the altitude of the airplane (opposite side of the triangle), we can apply the Pythagorean Theorem:

$c^2 = a^2 + b^2$

Where:

• $c$ is the hypotenuse (290 m),
• $a$ is the adjacent side (210 m),
• $b$ is the opposite side (the altitude we are solving for).

We rearrange the formula to solve for $b$:

$b = \sqrt{c^2 - a^2}$

Let's calculate that.The altitude of the plane is 200 meters.

Would you like further details or have any additional questions?

Here are five related questions to deepen understanding:

1. How can trigonometry be applied to find the angle of elevation of the plane?
2. What is the relationship between the angles in a right triangle when the sides are known?
3. How does the Pythagorean Theorem apply in 3D problems?
4. Can you calculate the total distance covered by the plane in the horizontal and vertical directions?
5. How would the altitude change if the hypotenuse increased but the adjacent side stayed the same?

Tip: The Pythagorean Theorem only applies to right-angled triangles!