Question

В прямоугольном треугольнике ABC угол А в 2 раза меньше угла B А гепотенуза АВ равна 18 см Найдите катет ВС

Answer 1

Подвьаьдвжцжжрбдщл двпдщьсщдрадбвбп

Answer 2

Problem Analysis

We are given a right triangle ABC, where angle A is twice as small as angle B, and the hypotenuse AB is equal to 18 cm. We need to find the length of side BC.

Solution

Let's denote the length of side BC as x.

According to the given information, we know that angle A is twice as small as angle B. This means that angle A is 1/3 of the total angle in the triangle, and angle B is 2/3 of the total angle.

Using the Pythagorean theorem, we can relate the lengths of the sides of a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the other two sides (BC and AC).

Applying the Pythagorean theorem to triangle ABC, we have:

AB^2 = BC^2 + AC^2

Substituting the given values, we get:

18^2 = x^2 + (2x)^2

Simplifying the equation, we have:

324 = x^2 + 4x^2

Combining like terms, we get:

5x^2 = 324

Dividing both sides by 5, we get:

x^2 = 64.8

Taking the square root of both sides, we get:

x = √64.8

x ≈ 8.05 cm

Therefore, the length of side BC is approximately 8.05 cm.

Answer

The length of side BC in the right triangle ABC is approximately 8.05 cm.