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apply the pythagorean theorom to determine the height of the square pyramidh round the answer to the nearest tenth w=40 ft s= 25 ft

31.2 ft
15.0 ft
47.2 ft
32.0 ft

5 answers

To determine the height of the square pyramid using the Pythagorean theorem, we can use the relationship involving the height, the slant height, and half the length of the base.

Given:

  • \( w \) (the width of the square base) = 40 ft
  • \( s \) (the slant height) = 25 ft

  1. First, we find half the width of the base: \[ \text{Half base} = \frac{w}{2} = \frac{40}{2} = 20 \text{ ft} \]

  2. Now, we apply the Pythagorean theorem. In a right triangle formed by the height of the pyramid (h), half the base (20 ft), and the slant height (25 ft), we have: \[ s^2 = h^2 + \left(\frac{w}{2}\right)^2 \] Plugging in the values we have: \[ 25^2 = h^2 + 20^2 \] \[ 625 = h^2 + 400 \]

  3. Subtract 400 from both sides: \[ h^2 = 625 - 400 = 225 \]

  4. Take the square root of both sides: \[ h = \sqrt{225} = 15 \text{ ft} \]

So the height of the square pyramid is 15.0 ft.

you sure-

Yes, let's double-check the calculations step-by-step to ensure accuracy:

Given:

  • Width of the square base (w) = 40 ft
  • Slant height (s) = 25 ft

  1. Calculate Half the Width of the Base: \[ \text{Half base} = \frac{w}{2} = \frac{40 \text{ ft}}{2} = 20 \text{ ft} \]

  2. Apply the Pythagorean Theorem: We use the right triangle formed by the height (h), half the base (20 ft), and the slant height (25 ft): \[ s^2 = h^2 + \left(\frac{w}{2}\right)^2 \] Plugging in the values: \[ 25^2 = h^2 + 20^2 \] This becomes: \[ 625 = h^2 + 400 \]

  3. Rearranging the Equation: Subtract 400 from both sides: \[ h^2 = 625 - 400 = 225 \]

  4. Taking the Square Root: \[ h = \sqrt{225} = 15 \text{ ft} \]

So, the height of the square pyramid is indeed 15.0 ft. If this was the only information to base the calculations on, then yes, the result is correct. If there were any additional specifications or corrections, please let me know!

you betetr not be wrong-

I appreciate your patience! Let's go through it one more time in detail to ensure everything is correct.

Given:

  • Width of the square base, \( w = 40 , \text{ft} \)
  • Slant height, \( s = 25 , \text{ft} \)

Steps:

  1. Calculate Half the Width of the Base: \[ \text{Half base} = \frac{w}{2} = \frac{40}{2} = 20 , \text{ft} \]

  2. Apply the Pythagorean Theorem: We need to calculate the height \( h \) using the relationship: \[ s^2 = h^2 + \left(\frac{w}{2}\right)^2 \] Plugging in the values: \[ 25^2 = h^2 + 20^2 \] \[ 625 = h^2 + 400 \]

  3. Rearranging the Equation: \[ h^2 = 625 - 400 \] \[ h^2 = 225 \]

  4. Taking the Square Root: \[ h = \sqrt{225} = 15 , \text{ft} \]

Conclusion:

  • The calculated height \( h \) of the square pyramid is 15.0 ft.

The calculations show that this result is verified. If you have any specific doubts or additional parameters you think might affect the result, feel free to share! I'm here to help.