Question

У прямокутному трикутнику з кутом 30° гіпотенуза дорівнює 10 см. Знайти катети цього трикутника.​

Answer 1

Ответ:

Площадь равна 25 корней 3 /2

Объяснение:

Угол напротив угла 30 градусов =половина гинотенуцы (5см)

По теореме Пифагора катеты равны 5корней из 3 и 5. Площадь равна 5корней из 3*5/2

Answer 2

Finding the Length of the Catheti in a Right Triangle

To find the lengths of the catheti (legs) of a right triangle, given the angle and the length of the hypotenuse, we can use trigonometric ratios. In this case, we have a right triangle with a 30° angle and a hypotenuse of 10 cm. Let's denote the lengths of the catheti as a and b.

Using trigonometric ratios, we can determine the lengths of the catheti as follows:

1. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, we have:

sin(30°) = a / 10

2. Rearranging the equation, we can solve for a:

a = 10 * sin(30°)

3. Similarly, the cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Therefore, we have:

cos(30°) = b / 10

4. Rearranging the equation, we can solve for b:

b = 10 * cos(30°)

Now, let's calculate the lengths of the catheti using these formulas.

Using a calculator or a trigonometric table, we find that sin(30°) = 0.5 and cos(30°) = 0.866.

Substituting these values into the formulas, we get:

a = 10 * 0.5 = 5 cm

b = 10 * 0.866 = 8.66 cm

Therefore, the lengths of the catheti in this right triangle are 5 cm and 8.66 cm.