Let’s solve each of these Pythagorean Theorem word problems step by step. The Pythagorean Theorem states:
>
a² + b² = c²
> where *a* and *b* are the legs of a right triangle, and *c* is the hypotenuse (the side opposite the right angle).
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Problem 1:
> Dan secures a ladder firmly to the wall to dust a photo frame mounted on the wall. The foot of the ladder is placed 6 feet from the wall. If the top of the ladder rests 8 feet up the wall, what is the length of the ladder?
Solution:
This forms a right triangle:
- One leg (distance from wall) = 6 ft
- Other leg (height on wall) = 8 ft
- Ladder = hypotenuse = ?
Use Pythagorean Theorem:
> c² = 6² + 8²
> c² = 36 + 64
> c² = 100
> c = √100 =
10 feet
✔ Answer: 10.0 feet
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Problem 2:
> If the playing surface of a carom board is a square of length 28 inches, what is the diagonal length of the playing surface?
Solution:
A square’s diagonal splits it into two right triangles. Each leg = 28 in.
> c² = 28² + 28²
> c² = 784 + 784 = 1568
> c = √1568 ≈ 39.597...
Rounded to nearest tenth:
39.6 inches
✔ Answer: 39.6 inches
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Problem 3:
> Carlos flies his drone 5 feet above the ground. He rotates the drone to the right. So far, the drone has flown a total of 12 feet. How far is the drone from the start point?
Solution:
This is a bit tricky — “flown a total of 12 feet” likely means horizontal distance traveled (since height is fixed at 5 ft). So we have:
- Vertical leg = 5 ft (altitude)
- Horizontal leg = 12 ft (distance moved sideways)
- Distance from start point = straight-line distance = hypotenuse
> c² = 5² + 12²
> c² = 25 + 144 = 169
> c = √169 =
13 feet
✔ Answer: 13.0 feet
*(Note: This is a classic 5-12-13 right triangle!)*
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Problem 4:
> A ship is on its maiden voyage to the mystery island. According to the map, it has to travel 99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest route that leads to the mystery island.
Solution:
The shortest route is the straight-line distance (hypotenuse) from start to finish.
- North leg = 99 mi
- West leg = 20 mi
> c² = 99² + 20²
> c² = 9801 + 400 = 10201
> c = √10201 =
101 miles
✔ Answer: 101.0 miles
*(Another classic: 20-99-101 triangle!)*
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Problem 5:
> For her boat model, Dahlia cut a piece of fabric in the shape of a right triangle. If the length of the longest side was 8 inches and one of other two sides measured 4 inches, what was the length of the other side?
Solution:
Longest side = hypotenuse = 8 in
One leg = 4 in
Find other leg = let’s call it *b*
Use Pythagorean Theorem:
> a² + b² = c²
> 4² + b² = 8²
> 16 + b² = 64
> b² = 64 - 16 = 48
> b = √48 ≈ 6.928...
Rounded to nearest tenth:
6.9 inches
✔ Answer: 6.9 inches
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##
✔ Final Answers:
1)
10.0 feet
2)
39.6 inches
3)
13.0 feet
4)
101.0 miles
5)
6.9 inches
All solved using the Pythagorean Theorem with rounding to the nearest tenth as instructed.
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem printable worksheet for 8th grade math.
