Question

If The Sides Of A Right-Angled Triangle Form An A.P. Then The Sines Of The Acute Angle Is____

Answer 1

The sides of a right triangle are in arithmetic progression.Let one of the legs be x, the other leg x+d, and the hypotenuse x+2d.

Then by the Pythagorean theorem we have:

`x^2+(x+d)^2=(x+2d)^2`

`x^2+x^2+2dx+d^2=x^2+4dx+4d^2`

`3d^2+2dx-x^2=0`

`(3d-x)(d+x)=0`

`==>3d=x` or `d=-x`

We want the ratio of the legs or `x/(x+d)`

If `d=-x` this makes no sense in the problem as one of the sides has length 0.

`3d=x==>x/(x+d)=(3d)/(3d+d)=3/4`

So the ratio of sides is 3:4.

     

Step-by-step explanation: