A right-angled triangle is given, and it is also known that one of the acute angles of the triangle is 2/3 of the other.
To find the acute angles of a triangle, let us first recall the theorem on the sum of the angles of a triangle. It says that the sum of the angles of the triangle is 180 °.
Let’s designate one of the acute angles of the triangle using the variable x °, then the second can be written as 2 / 3x °.
Let’s solve a linear equation with one variable:
x + 2 / 3x + 90 = 180;
5 / 3x = 180 – 90;
5 / 3x = 90;
x = 54 °.
So, one of the acute angles is 54 °, and the second is 2/3 * 54 = 36 °
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