In a right-angled triangle PTK, angle T = 90 °. PT = 7√3 KT = 7cm find the angle K and the hypotenuse KP.

1. Applying the formula of the Pythagorean theorem, we calculate the length of the RK hypotenuse:

RK = √KT ^ 2 + PT ^ 2 = √7 ^ 2 + (7√3) ^ 2 = √49 + 49 x 3 = √196 = 14 cm.

2. The length of the CT leg, located opposite the angle P, is equal to half the length of the RK hypotenuse.

(CT / RK = 7: 14 = 1/2). Therefore, the angle P is equal to 30 ° (according to the properties of a right-angled triangle).

3. We calculate the value of the angle K, taking into account that the total value of all internal angles of the triangle is 180 °:

Angle K = 180 ° – 90 ° – 30 ° = 60 °.

Answer: Angle K = 60 °, RK = 14 cm.