In a right-angled triangle MKC, it is known that the angle is M = 90 degrees, angle C = 60, CM = 7 cm.

In a right-angled triangle MKC, it is known that the angle is M = 90 degrees, angle C = 60, CM = 7 cm. Find the hypotenuse CK.

Given: rectangular △ MKC, ∠M = 90 °, ∠C = 60 °, CM = 7 cm.
Find: hypotenuse СK.
Using the theorem on the sum of the angles of a triangle (equal to 180 °), we find the angle K.
We have:
K = 180 ° – (∠M + ∠C) = 180 ° – (90 ° + 60 °) = 180 ° – 150 ° = 30 °.
This means that the degree measure of kuta K is 30 °.
Now, proceeding from the property of a right-angled triangle, which reads: “a leg opposite to an angle of 30 ° is equal to half of the hypotenuse”, we find the hypotenuse CK.
We have:
CM = 1/2 * CK.
Hence:
CK = CM * 2 = 7 * 2 = 14 (cm).
Answer: The hypotenuse CK △ MKC is 14 cm.