Question

В прямоугольном треугольнике АВС с прямым углом В катет АВ равен 8 см, а противолежащий угол С равен 30*. Найдите гипотенузу АС.Зарание огромное спасибо

Answer 1

Решение смотри на фото)

Answer 2

Finding the Hypotenuse of a Right Triangle

To find the length of the hypotenuse (AC) in a right triangle ABC, where angle C is 30 degrees and side AB is 8 cm, we can use trigonometric ratios.

The trigonometric ratio that relates the length of the hypotenuse to the length of the adjacent side is the cosine function. In this case, we can use the cosine function to find the length of AC.

The cosine of an angle is equal to the adjacent side divided by the hypotenuse. Therefore, we can write the equation as:

cos(C) = AB / AC

Substituting the given values, we have:

cos(30) = 8 / AC

To solve for AC, we can rearrange the equation:

AC = 8 / cos(30)

Now, let's calculate the value of AC.

Using a calculator, we find that the cosine of 30 degrees is approximately 0.866.

AC = 8 / 0.866 ≈ 9.24 cm

Therefore, the length of the hypotenuse AC is approximately 9.24 cm.

Please note that the calculations provided are based on the given information and assumptions.