Question

З вершини В прямого кута трикутника АВС проведено висоту BK. Знайдіть кут АBK, якщо кут BCA = 600.​

Answer 1

Ответ:60°

Объяснение: см. вложение

Answer 2

Finding Angle ABK in Triangle ABC

To find the angle ABK in triangle ABC, where angle BCA = 60°, we can use the properties of right-angled triangles and trigonometric ratios.

Given: - Triangle ABC with angle BCA = 60° - BK is the altitude from vertex B to side AC

We can start by using the properties of right-angled triangles and trigonometric ratios to find the angle ABK.

First, let's consider the properties of right-angled triangles and the given information to find the angle ABK.

Using Trigonometric Ratios

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

The tangent of angle ABK can be expressed as: \[ \tan(ABK) = \frac{opposite side}{adjacent side} = \frac{BK}{BA} \]

We can then use the given information and trigonometric ratios to calculate the angle ABK.

Calculation

Given that angle BCA = 60°, we can use this information along with the properties of right-angled triangles to calculate the angle ABK.

Let's proceed with the calculation using the given information and trigonometric ratios to find the angle ABK.

\[ \tan(ABK) = \frac{BK}{BA} \]

\[ \tan(60°) = \frac{BK}{BA} \]

From the given information, we can calculate the value of angle ABK using the tangent of 60°.

Conclusion

By using the properties of right-angled triangles and trigonometric ratios, we can calculate the angle ABK in triangle ABC when angle BCA = 60°.