In the triangle KСР (KС = СР) the angle С = 68 degrees, KС = 12 cm.Find the length КР.

Given:
isosceles triangle KCP;
KС = CP;
angle C = 68 degrees;
КС = 12 centimeters.
Find the length of KP -?
Solution:
1) Consider an isosceles triangle KCP. The sum of the degree measures of the angles of any triangle is 180 degrees.
Then the angle K + the angle P = 180 – 68 = 112 degrees;
angle K = angle P = 112: 2 = 56 degrees;
2) By the sine theorem
КP / sin С = КС / sin Р;
KP / sin 68 degrees = 12 / sin 56 degrees;
KP = (12 * sin 68 degrees) / sin 56 degrees.
Answer: KP = (12 * sin 68 degrees) / sin 56 degrees.