Текст. Теорема Пифагора

Теорема Пифагора подана на английском языке, с иллюстрациями и графическими элементами
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The Pythagorean Theorem.

Теорема Пифагора.






This theorem states that, in a right triangle, the square of the length of the longest side, or hypotenuse, is equal to the sum of the squares of the other two sides. Algebraically, the Pythagorean theorem is written a2 + b2 = с2, where с is the hypotenuse.

So in the right triangle, if а = 3 and с = 5, can you determine the length of b? Start with the formula a2 + b2 =  c2 and substitute in the values you know.






Exercise 2. Решите и пропишите примеры 1 или 2 на английском.





Exercise 3. Ознакомьтесь с примерами из жизни, переведите их на русский язык. Learn life examples.

  • Zedekiah is building a gate. It is to be five feet tall and eight feet wide. If the gate is "square" (that is, if the sides meet at the corners to form right angles), what will be the length of the diagonal bracing wire? Round to the nearest quarter-inch.

The width (going horizontally), the height (going vertically), and the wire (going diagonally across) for the gate, form a right triangle. When the gate is square, the diagonal will obey the Pythagorean Theorem.

52 + 82 = c2 
25 + 64 = 89 = c2 
c = sqrt[89] = 9.43398 (approximately) 

So the bracing wire will be nine feet long, plus another 0.43389 feet or so. There are twelve inches in one foot, so:

0.43389 × 12 = 5.20776

There will be another about 5.2 inches; 0.2 is closer to 0.25 than to 0.0, so:

The length of the wire will be 9 feet, 5 1/4 inches.


  • Zedekiah needs to find the width of the pond on a plot of land he's selling. He has made measurements to point R from points P and Q on either side of the pond, and is certain that the angle at P is right, as displayed:

Assuming his measurements are correct, what is the width of the pond?

I have two sides of what is to be assumed to be a right triangle, so I can apply the Pythagorean Theorem to find the length of the third side. Since the angle at P is the (assumed) right angle, then QR is the hypotenuse, and:


pond; P on left, Q on right, PQ horizontal; R below; PR vertical, |PR| = 24; QR diagonal, |QR| = 26



262 = 242 + |PQ|2 
676 = 576 + |PQ|2 
100 = |PQ|2 
10 = |PQ|                                    


The pond is ten meters across.



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Английский язык, СУЗ, Разное