Given a right-angled triangle CDE, where DE is the hypotenuse.

Given a right-angled triangle CDE, where DE is the hypotenuse. The outer angle at the vertex D is 120, the side of CD is 5 cm. What is the hypotenuse.

We find out what value the angle D of the specified triangle will equal if from the condition of our problem we know for sure that the external angle is 120 °:

180 – 120 = 60.

Let’s find out what value the length of the hypotenuse will equal, which, according to the condition of the task, is the DE side, if we know that the length of the CD side is 5 centimeters:

CD / DE = cos D;

DE = CD: cos D;

DE = 5: cos 60 °;

DE = 5: 1/2;

DE = 10.

Answer: Under these initial conditions, the length of the DE hypotenuse will be 10 centimeters.