Question

Найдите катет АС прямоугольного треугольника АВС(угол С-прямой),если ВС=12 и уголА=30 гразусам ?

Answer 1

По теореме катет, лежащий против угла в 30 градусов, равен половине гипотинузы. Тогда AB = 2 CB = 24 см.
По теореме Пифагора
AB² = AC² + CB²
AC = √ AB² - CB² = √576 - 244 = √ 332 см

Answer 2

Finding the Length of Side AC in a Right-Angled Triangle

To find the length of side AC in the right-angled triangle ABC, where angle C is the right angle, side BC is 12, and angle A is 30 degrees, we can use trigonometric functions.

Using Trigonometric Functions to Find Side AC

We can use the trigonometric function tangent to find the length of side AC. The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side.

The formula for finding the length of side AC using the tangent function is:

tan(A) = opposite / adjacent

Where: - A = angle A - opposite = side opposite to angle A (side BC in this case) - adjacent = side adjacent to angle A (side AC in this case)

Calculating the Length of Side AC

Given that angle A is 30 degrees and side BC is 12, we can use the tangent function to find the length of side AC.

tan(30°) = BC / AC

Now, we can solve for AC:

AC = BC / tan(30°)

Calculating the Value of AC

Let's calculate the value of side AC using the given values:

AC = 12 / tan(30°)

Using a calculator, we find:

AC ≈ 20.78

So, the length of side AC in the right-angled triangle ABC is approximately 20.78 units.

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