One of the corners of a right-angled triangle is 60 degrees, and the sum of the hypotenuse

One of the corners of a right-angled triangle is 60 degrees, and the sum of the hypotenuse and the smaller leg is 30 cm. Find the hypotenuse of the triangle.

Given:

Right angle triangle MKC

angle M = 90 degrees,

angle C = 60 degrees,

CM + KC = 30 centimeters.

Find the length of the hypotenuse CK -?

Decision:

1) Consider a right-angled triangle MKC. We know that the sum of the degree measures of any triangle is 180 degrees. Hence:

angle K = 180 – (angle M + angle C);

angle K = 180 – (90 + 60);

angle K = 180 – 150;

angle K = 30 degrees;

2) In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then MS = 1/2 * KC;

KS = 2 * MS.

We know that MC + KC = 30.

Then MC + 2 * MC = 30;

3 * MC = 30;

MC = 30: 3;

MC = 10 centimeters;

KC = 2 * 10;

KC = 20 centimeters.

Answer: 20 centimeters.