Find the acute angles of a right-angled triangle if you know that one angle is 60 degrees greater than the other?

Let the smaller of the acute angles of our right-angled triangle be equal to the variable a.

Then, according to the condition of the problem, it will be possible to represent the largest of the acute angles in terms of a + 60.

Since we know from the school geometry course that the sum of such angles is always 90 °, then it is possible to write down an equation and find out what each of the angles will be equal to:

a + a + 60 = 90;

2a = 30;

a = 15;

90 – 15 = 75.

Answer: The smaller acute angle will be 15 °, and the larger acute angle will be 75 °.