Question

ВК- бісектриса трикутника АВС. Знайти кут А, якщо кут С дорівнює 35°, кут ВКС= 105°.

Answer 1

Ответ:

Ответ 65

Объяснение:

Объяснерие на фото

Answer 2

Finding the Angle A of Triangle ABC

To find the angle A of triangle ABC when angle C is 35° and angle BKC is 105°, we can use the fact that the angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.

Let's denote the length of segment AB as x and the length of segment AC as y. Since the angle bisector divides the opposite side into segments that are proportional to the adjacent sides, we can set up the following proportion:

x/y = BC/AC

Now, let's use the given information to solve for the angle A.

From the given information, we know that angle C is 35° and angle BKC is 105°. Since angle BKC is an exterior angle of triangle ABC, it is equal to the sum of angles B and C. Therefore, we can write:

angle B + angle C = angle BKC angle B + 35° = 105° angle B = 105° - 35° angle B = 70°

Now, let's use the Law of Sines to relate the angles and sides of triangle ABC. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In other words:

BC/sin(angle B) = AC/sin(angle C)

Substituting the known values, we have:

BC/sin(70°) = AC/sin(35°)

Now, let's solve for BC in terms of AC:

BC = (AC * sin(70°)) / sin(35°)

Since we know that x/y = BC/AC, we can substitute BC with the expression we just found:

x/y = [(AC * sin(70°)) / sin(35°)] / AC

Simplifying the expression:

x/y = sin(70°) / sin(35°)

Now, we can solve for x/y:

x/y = sin(70°) / sin(35°) x/y = 1.93185165258 / 0.57357643635 x/y ≈ 3.366

Therefore, the ratio of the lengths of segments AB and AC is approximately 3.366.

To find the angle A, we can use the inverse tangent function:

angle A = arctan(x/y) angle A = arctan(3.366)

Using a calculator, we find that angle A is approximately 72.9°.

So, the angle A of triangle ABC is approximately 72.9° when angle C is 35° and angle BKC is 105°.

Conclusion

In this response, we used the concept of the angle bisector of a triangle and the Law of Sines to find the angle A of triangle ABC when angle C is 35° and angle BKC is 105°. We found that angle A is approximately 72.9°.