Question

Дан прямоугольный треугольник ABC. известно, что гипотенуза равна 18см и <ABC =30°. найди катет AC. ответ дать в сантиметрах​

Answer 1

Объяснение:

Катет, лежащий против угла в тридцать градусов, равен половине гипотенузы.
AC=18/2=9см.
Можно лучший ответ, пожалуйста?

Answer 2

Problem Analysis

We are given a right triangle ABC, where the hypotenuse AB is 18 cm and angle ABC is 30 degrees. We need to find the length of the leg AC.

Solution

To find the length of the leg AC, we can use the trigonometric relationship between the sides of a right triangle. In this case, we can use the sine function.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In our case, the side opposite angle ABC is AC and the hypotenuse is AB.

Using the sine function, we can write the following equation:

sin(ABC) = AC / AB

Substituting the given values, we have:

sin(30°) = AC / 18 cm

To find the value of sin(30°), we can refer to a trigonometric table or use a calculator. The value of sin(30°) is 0.5.

Substituting this value into the equation, we have:

0.5 = AC / 18 cm

To find the value of AC, we can rearrange the equation:

AC = 0.5 * 18 cm

Simplifying, we get:

AC = 9 cm

Therefore, the length of the leg AC is 9 cm.

Answer

The length of the leg AC is 9 cm.