In a right-angled triangle ABC on leg AC, point K is taken so that the angle BKC

In a right-angled triangle ABC on leg AC, point K is taken so that the angle BKC is equal to the angle B. Find the hypotenuse AB if CK = 4.5, AK = 3.5

1. Calculate the length of the speaker side:

AC = 3.5 + 4.5 = 8 centimeters.

2. Angle B = 90 – angle BKC, Angle A = 90 – angle B.

3. Angle B is equal to the angle BKC by condition. Therefore, the angle A is equal to the angle B. Therefore, the triangle

ABC is isosceles, and its sides BC and AC, which are the legs of a right triangle, are equal:

BC = AC = 8 centimeters.

4. Applying the Pythagorean theorem, we calculate the length of the hypotenuse AB:

AB = √AC ^ 2 + BC ^ = √8 ^ 2 + 8 ^ 2 = √2 x 8 ^ 2 = 8√2 centimeters.

Answer: the length of the hypotenuse AB is 8√2 centimeters.