The image presents a real-world scenario involving the
Pythagorean Theorem, which is a fundamental principle in geometry. Let's break down the problem and solve it step by step.
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🔍 Understanding the Scenario
- A firefighter is using a ladder to rescue someone from a second-story window.
- The
ladder (hypotenuse) is placed against the house, forming a right triangle.
- The
height of the wall (vertical leg) is
40 feet.
- The
distance from the base of the ladder to the house (horizontal leg) is
60 feet.
- We are asked to find the
length of the ladder, labeled as
x.
This forms a
right triangle where:
- One leg = 40 ft (height)
- Other leg = 60 ft (base)
- Hypotenuse = x (ladder length)
---
📐 Pythagorean Theorem
The Pythagorean Theorem states:
$$
a^2 + b^2 = c^2
$$
Where:
- $ a $ and $ b $ are the legs of the right triangle,
- $ c $ is the hypotenuse.
Let’s plug in the values:
$$
40^2 + 60^2 = x^2
$$
$$
1600 + 3600 = x^2
$$
$$
5200 = x^2
$$
Now take the square root of both sides:
$$
x = \sqrt{5200}
$$
$$
x \approx 72.11 \text{ feet}
$$
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✔ Answer:
The length of the ladder is approximately
72.11 feet.
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💡 What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
It's used in many real-life applications like construction, navigation, and physics — just like in this fire rescue scenario!
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🧠 Summary:
-
Given: 40 ft height, 60 ft base
-
Find: Ladder length (hypotenuse)
-
Formula: $ a^2 + b^2 = c^2 $
-
Result: $ x \approx 72.11 $ ft
So, the ladder must be about
72.11 feet long to reach the window safely.
Parent Tip: Review the logic above to help your child master the concept of real life pythagorean theorem examples.
