To find out how far the plane needs to travel before it lands, we can model this situation using a right-angled triangle.
1. Identify the sides of the triangle:
* The height of the plane is one side (let's call it $a$). The problem gives this as 5200 m. Since the other distance is in kilometers, we should convert this to km:
$$5200 \text{ m} = 5.2 \text{ km}$$
* The horizontal distance to the airport is the second side (let's call it $b$). This is given as $10.2 \text{ km}$.
* The distance the plane travels through the air is the hypotenuse (the longest side, let's call it $c$). This is what we need to find.
2. Use the Pythagorean theorem:
The formula for a right-angled triangle is:
$$a^2 + b^2 = c^2$$
Substitute the values we know into the formula:
$$5.2^2 + 10.2^2 = c^2$$
3. Perform the calculations:
First, square the numbers:
* $5.2 \times 5.2 = 27.04$
* $10.2 \times 10.2 = 104.04$
Next, add these two results together:
$$27.04 + 104.04 = 131.08$$
So, $c^2 = 131.08$.
4. Find the final distance ($c$):
To find $c$, we need to take the square root of 131.08:
$$c = \sqrt{131.08}$$
$$c \approx 11.44901...$$
5. Round the answer:
The question asks for the answer to 1 decimal place (1dp).
Looking at the second decimal digit (4), it is less than 5, so we round down (keep the first decimal digit as it is).
$$c \approx 11.4 \text{ km}$$
Final Answer:
11.4 km
Parent Tip: Review the logic above to help your child master the concept of real life pythagorean theorem examples.
