Question

use a pythagorean triple to find the value of x.
7.
8.
9.
10.
11.
12.
example 3

1. construction the bottom end of a ramp at a warehouse is 10 feet from the base of the main dock, and the ramp is 11 feet long.

how high is the dock?

Explanation:

Problem 7: Step1: Apply Pythagorean theorem

$x^2 + 8^2 = 17^2$

Problem 7: Step2: Calculate known squares

$x^2 + 64 = 289$

Problem 7: Step3: Isolate $x^2$

$x^2 = 289 - 64 = 225$

Problem 7: Step4: Solve for x

$x = \sqrt{225} = 15$

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Problem 8: Step1: Apply Pythagorean theorem

$24^2 + 45^2 = x^2$

Problem 8: Step2: Calculate known squares

$576 + 2025 = x^2$

Problem 8: Step3: Sum and solve for x

$x^2 = 2601, \quad x = \sqrt{2601} = 51$

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Problem 9: Step1: Apply Pythagorean theorem

$28^2 + 96^2 = x^2$

Problem 9: Step2: Calculate known squares

$784 + 9216 = x^2$

Problem 9: Step3: Sum and solve for x

$x^2 = 10000, \quad x = \sqrt{10000} = 100$

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Problem 10: Step1: Apply Pythagorean theorem

$5^2 + 12^2 = x^2$

Problem 10: Step2: Calculate known squares

$25 + 144 = x^2$

Problem 10: Step3: Sum and solve for x

$x^2 = 169, \quad x = \sqrt{169} = 13$

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Problem 11: Step1: Apply Pythagorean theorem

$x^2 + 8^2 = 10^2$

Problem 11: Step2: Calculate known squares

$x^2 + 64 = 100$

Problem 11: Step3: Isolate $x^2$

$x^2 = 100 - 64 = 36$

Problem 11: Step4: Solve for x

$x = \sqrt{36} = 6$

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Problem 12: Step1: Apply Pythagorean theorem

$12^2 + x^2 = 20^2$

Problem 12: Step2: Calculate known squares

$144 + x^2 = 400$

Problem 12: Step3: Isolate $x^2$

$x^2 = 400 - 144 = 256$

Problem 12: Step4: Solve for x

$x = \sqrt{256} = 16$

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Problem 13: Step1: Apply Pythagorean theorem

$h^2 + 10^2 = 11^2$ (h = dock height)

Problem 13: Step2: Calculate known squares

$h^2 + 100 = 121$

Problem 13: Step3: Isolate $h^2$

$h^2 = 121 - 100 = 21$

Problem 13: Step4: Solve for h

$h = \sqrt{21} \approx 4.58$

Answer:

1. $x=15$
2. $x=51$
3. $x=100$
4. $x=13$
5. $x=6$
6. $x=16$
7. The dock is $\sqrt{21}$ (or ~4.58) feet high