Here are the step-by-step solutions for each problem on the worksheet.
1. Find the hypotenuse of a triangle with a base of 11 cm and height of 9 cm.
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Step 1: Use the Pythagorean theorem: $a^2 + b^2 = c^2$. Here, $a = 11$ and $b = 9$.
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Step 2: Square the numbers: $11^2 = 121$ and $9^2 = 81$.
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Step 3: Add them together: $121 + 81 = 202$.
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Step 4: Find the square root of 202 to get $c$. $\sqrt{202} \approx 14.21$.
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Answer: The hypotenuse is approximately
14.21 cm.
2. Tommy the Turtle wants to be in the "T". ... How far away from the "T" exactly how far is Tommy the Turtle from his goal?
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Step 1: Identify the distances. The horizontal distance (along the grass) is 1 mile. The vertical distance (up the tree) is 1.2 miles.
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Step 2: These form a right triangle where the direct path is the hypotenuse ($c$).
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Step 3: Use the formula: $1^2 + 1.2^2 = c^2$.
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Step 4: Calculate squares: $1 + 1.44 = 2.44$.
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Step 5: Find the square root: $\sqrt{2.44} \approx 1.56$.
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Answer: Tommy is approximately
1.56 miles away from the "T".
3. Tom is afraid of heights... ladder is 10 feet long... placed 8 feet from the deck... how high above the ground does the ladder touch the deck?
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Step 1: The ladder is the hypotenuse ($c = 10$). The distance from the wall is one leg ($a = 8$). We need to find the height ($b$).
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Step 2: Rearrange the formula: $a^2 + b^2 = c^2$ becomes $8^2 + b^2 = 10^2$.
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Step 3: Calculate squares: $64 + b^2 = 100$.
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Step 4: Subtract 64 from 100: $b^2 = 36$.
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Step 5: Find the square root of 36: $b = 6$.
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Answer: The ladder touches the deck
6 feet above the ground.
4. Maria walked 3 km west and 4 km south. Calculate how far she is from her starting point.
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Step 1: West and South form a right angle. The legs are 3 and 4.
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Step 2: Use the formula: $3^2 + 4^2 = c^2$.
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Step 3: Calculate squares: $9 + 16 = 25$.
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Step 4: Find the square root of 25: $c = 5$.
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Answer: She is
5 km from her starting point.
5. Lane's guest house is 15 m long and 12 m wide. How long is the diagonal of the room?
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Step 1: The length and width are the legs of the triangle. $a = 15$, $b = 12$.
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Step 2: Use the formula: $15^2 + 12^2 = c^2$.
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Step 3: Calculate squares: $225 + 144 = 369$.
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Step 4: Find the square root of 369: $\sqrt{369} \approx 19.21$.
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Answer: The diagonal is approximately
19.21 meters.
6. David leaves the house... walks 205 m west and 125 m north. Rounded to the nearest whole number...
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Step 1: The legs are 205 and 125.
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Step 2: Use the formula: $205^2 + 125^2 = c^2$.
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Step 3: Calculate squares: $42,025 + 15,625 = 57,650$.
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Step 4: Find the square root of 57,650: $\sqrt{57,650} \approx 240.1$.
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Step 5: Round to the nearest whole number: 240.
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Answer: David is
240 meters from the starting point.
7. Laptop screen sizes... diagonal portion... 10 inch width and 8 inches height. Calculate the screen size.
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Step 1: The width and height are the legs. $a = 10$, $b = 8$.
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Step 2: Use the formula: $10^2 + 8^2 = c^2$.
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Step 3: Calculate squares: $100 + 64 = 164$.
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Step 4: Find the square root of 164: $\sqrt{164} \approx 12.8$.
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Answer: The screen size is approximately
12.8 inches.
Final Answer:
1. 14.21 cm
2. 1.56 miles
3. 6 feet
4. 5 km
5. 19.21 m
6. 240 m
7. 12.8 inches
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem word problems independent practice worksheet answer key.
