Question

В треугольнике ABC угол C=90 , AB=12. Внешний угол при вершине B равен 120 .Найдите BC

Answer 1

Тк внешний угол равен 120,то уголВ=180-120=60°. Тогда уголА=90-60=30°. Тк катет,лежащий против угла 30° равен половине гипотенузы,то СВ=12/2=6 Ответ:6

Answer 2

Given Information:

We are given a triangle ABC with angle C equal to 90 degrees, AB measuring 12 units, and the external angle at vertex B measuring 120 degrees.

Approach to solve the problem:

To find the length of BC, we can use the concept of the trigonometric ratios in a right-angled triangle. Specifically, we can use the sine and cosine ratios to relate the angles and sides of the triangle.

Solution:

Let's analyze the given triangle ABC and break down the problem step by step.

1. Angle C is a right angle, which means side AC is the hypotenuse of the triangle. 2. We are given the length of side AB, which is 12 units. 3. The external angle at vertex B is 120 degrees, which means the internal angle at vertex B is 180 - 120 = 60 degrees.

Now, we can apply trigonometric ratios to find the length of BC.

Using the sine ratio: sin(B) = BC / AB

Since angle B is an internal angle, we will use the sine ratio: sin(60) = BC / 12

Simplifying the equation: BC = 12 * sin(60) BC = 12 * √3 / 2 BC = 6√3 units

Therefore, the length of side BC is 6√3 units.

Answer:

The length of side BC in triangle ABC is 6√3 units.