In a right angled triangle, two of the angles are in the ratio 6:13. Find the 3rd angle

To find the third angle of a right-angled triangle, we need to know one of the other two angles.

Given that the ratio of the angles in the triangle is 6:13, let's denote the angles as 6x, 13x, and 90 degrees, where x is a common factor.

Since the three angles of any triangle add up to 180 degrees, we can write the equation:

6x + 13x + 90 = 180

Combine like terms:

19x + 90 = 180

Subtract 90 from both sides:

19x = 180 - 90
19x = 90

Divide both sides by 19:

x = 90 / 19
x ≈ 4.737

So, the third angle is:

6x = 6 * 4.737
≈ 28.421

Therefore, the third angle of the right-angled triangle is approximately 28.421 degrees.

so, if the acute angles are 6x and 13x, that means that

6x+13x=90
x = 90/19
and the other two angles are
540/19 and 1170/19

or, we might have

90=13x, so one of the other angles is 6x, and we have the third angle z as

90 + (6/13)(90) + z = 180
z = 630/13

Why cannot 90 be 6x?