Explanation:
Let’s solve each problem one by one, using the Pythagorean Theorem:
a² + b² = c², where *c* is the hypotenuse (the longest side, opposite the right angle), and *a* and *b* are the other two sides.
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Problem 1:
Dan secures a ladder to the wall. The foot of the ladder is 6 ft from the wall, and the top rests 8 ft up the wall.
So we have a right triangle:
- One leg = 6 ft (distance from wall)
- Other leg = 8 ft (height on wall)
- Hypotenuse = length of ladder = ?
Use Pythagorean Theorem:
c² = 6² + 8² = 36 + 64 = 100
c = √100 = 10 ft
Rounded to nearest tenth:
10.0 ft
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Problem 2:
The playing surface is a square with side length 28 inches. The diagonal splits the square into two right triangles.
Each leg = 28 in
Diagonal = hypotenuse:
c² = 28² + 28² = 784 + 784 = 1568
c = √1568 ≈ ?
Let’s compute:
√1568 = √(16 × 98) = 4√98
√98 ≈ 9.899
So 4 × 9.899 ≈ 39.596
Rounded to nearest tenth:
39.6 inches
(Alternatively, use calculator: √1568 ≈ 39.597979 → 39.6)
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Problem 3:
Carlos flies his drone 5 ft above ground, and it has flown 12 ft total (this is the hypotenuse). We want horizontal distance from start point (the base of the right triangle).
So:
- Vertical leg = 5 ft
- Hypotenuse = 12 ft
- Horizontal leg = ? = x
x² + 5² = 12²
x² + 25 = 144
x² = 144 − 25 = 119
x = √119 ≈ 10.9087
Rounded to nearest tenth:
10.9 ft
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Problem 4:
Ship travels 99 miles north, then 20 miles west. Shortest route is straight line (hypotenuse) from start to end.
So legs: 99 mi and 20 mi
c² = 99² + 20² = 9801 + 400 = 10201
c = √10201 = ?
Note: 101² = 10201 exactly!
So c = 101 miles
Rounded to nearest tenth:
101.0 miles
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Problem 5:
Right triangle fabric piece. Longest side = 8 inches (so that’s the hypotenuse). One other side = 4 inches. Find the third side.
Let unknown side = x
Then:
x² + 4² = 8²
x² + 16 = 64
x² = 48
x = √48 = √(16×3) = 4√3 ≈ 4 × 1.732 = 6.928
Rounded to nearest tenth:
6.9 inches
Final Answer:
1) 10.0
2) 39.6
3) 10.9
4) 101.0
5) 6.9
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem word problems worksheet with answers.
