Let's solve the problem step by step using the
Pythagorean Theorem.
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🔹 Problem:
The mast of a fishing boat is 20 feet tall, and a rope runs from the top of the mast to the deck, attaching 15 feet away from the base of the mast. We are to find the length of the rope.
This forms a
right triangle, where:
- One leg = height of the mast =
20 feet
- Other leg = distance from base to where rope attaches =
15 feet
- The rope is the
hypotenuse (the side opposite the right angle)
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🔹 Pythagorean Theorem:
For a right triangle:
$$
a^2 + b^2 = c^2
$$
Where:
- $ a $ and $ b $ are the legs
- $ c $ is the hypotenuse
Let’s plug in the values:
$$
20^2 + 15^2 = c^2
$$
$$
400 + 225 = c^2
$$
$$
625 = c^2
$$
Now take the square root of both sides:
$$
c = \sqrt{625} = 25
$$
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✔ Answer:
The rope is
25 feet long.
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📌 Summary:
Using the Pythagorean Theorem, we found that the hypotenuse (rope) is 25 feet long when the two legs are 20 ft and 15 ft.
$$
\boxed{25} \text{ feet}
$$
Parent Tip: Review the logic above to help your child master the concept of word problems involving pythagorean theorem.
