In a right-angled triangle ABC with a hypotenuse AC, the outer angle at the apex is A = 120

In a right-angled triangle ABC with a hypotenuse AC, the outer angle at the apex is A = 120 degrees, AB = 5cm. Find the length of the hypotenuse of the triangle.

The outer and inner corners are adjacent. Knowing that the sum of adjacent angles is 180 °, we find the inner angle at the vertex A of the triangle ABC.
BAC angle = 180 ° – 120 ° = 60 °

In a right-angled triangle ABC, the BAC angle and the BCA angle are complementary up to 90 °.
Find the angle of the BCA 90 ° – 60 ° = 30 °.
By the property of the leg, which lies opposite the angle of 30 °, we find the hypotenuse, which will be twice as large as this leg.
AC = 2 * AB = 2 * 5 = 10 cm.
Answer: the length of the hypotenuse is 10 cm.