One of the right-angled triangle is 60, and the difference between the hypotenuse and the smaller leg

One of the right-angled triangle is 60, and the difference between the hypotenuse and the smaller leg is 15 find the hypotenuse.

Let us denote the hypotenuse by c and the leg by a. Since the triangle is rectangular, the equality is true:

a = c * cos (60) = c * √3 / 2.

c – a = 15 – according to the problem statement.

a = c – 15.

Substituting the expressed a into the 1st equality, we get:

c – 15 = c * √3 / 2;

c * (1 – √3 / 2) = 15;

c = 30 / (2 – √3).