Question

найдите катеты прямоугольного треугольник, если гипотенуза и один из углов соответственно равны 12 см и 45 градусов

Answer 1

AB и BC у меня катеты. Так как один из углов равен 45, то и другой угол будет равен 45 градусам, потому что сумма углов треугольника 180. Следовательно треугольник не только прямоугольный, но и равнобедренный. Значит AB=BC. Пусть АВ=ВС=х, тогда по теореме Пифагора х в квадрате + х в квадрате = 144, отсюда х=корень из 72 или 6 корней из 2. Это и будет ответ.

Answer 2

Finding the Catheti of a Right-Angled Triangle

To find the catheti of a right-angled triangle when the hypotenuse and one of the angles are given, we can use trigonometric functions. In this case, the hypotenuse is 12 cm, and one of the angles is 45 degrees.

Using Trigonometric Functions

We can use the trigonometric functions to find the lengths of the catheti. The sine and cosine functions are particularly useful in this case.

The sine of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Calculation

Using the given information, we can calculate the lengths of the catheti using the sine and cosine functions.

Let's denote the length of the catheti adjacent to the 45-degree angle as a and the length of the other cathetus as b.

We can use the following trigonometric relationships: - sin(45°) = a / 12 - cos(45°) = b / 12

Solution

Using the trigonometric relationships, we can solve for the lengths of the catheti: - sin(45°) = a / 12 - cos(45°) = b / 12

From the search results, we find that the sine of 45 degrees is approximately 0.7071 and the cosine of 45 degrees is also approximately 0.7071.

Substituting these values into the equations: - 0.7071 = a / 12 - 0.7071 = b / 12

Solving for a and b: - a ≈ 0.7071 * 12 ≈ 8.49 cm - b ≈ 0.7071 * 12 ≈ 8.49 cm

Conclusion

Therefore, the lengths of the catheti of the right-angled triangle are approximately 8.49 cm each.