Question

the acute angles of a right triangle are in the ratio 2:3find the angles of the triangle

Answer 1

It's a right angle triangle , so we know that one angle will be of 90° and sum of remaining two will be of 90°

So we can write from the above ratio, 2x+3x = 90

we get the value of x = 18

now we can find the angles, 2x = 36° and 3x= 54°

so remaining acute angles are 36° and 54°

Answer 2

let the angles be -
x and y.
according to question ...
x : y = 2 : 3
3x = 2y
x = 2y/3.
now,
since the triangle is right angled.
therefore,
x + y + 90 = 180 (angel sum property)
2y/3 + y = 90
5y/3 = 90
5y = 270
y = 54
hence
x = 36