In a right-angled triangle PKT (angle T = 90 degrees), PT = 7 √ 3 cm, KT = 7 cm.

In a right-angled triangle PKT (angle T = 90 degrees), PT = 7 √ 3 cm, KT = 7 cm. Find the angle K and the hypotenuse KP.

Since the triangle PKT is rectangular, then by the Pythagorean theorem we determine the length of the hypotenuse KP.

KP ^ 2 = PT ^ 2 + KT ^ 2 = (7 * √3) ^ 2 + 7 ^ 2 = 147 + 49 = 196.

KR = 14 cm.

Since the length of the KP hypotenuse is twice the length of the KT leg, the angle against the KT leg is 30. The TPK angle is 30.

The sum of the acute angles of a right-angled triangle is 90, then the angle РKТ = 90 – 30 = 60.

Answer: The length of the hypotenuse is 14 cm, the angle K is 60.