Question

if the sides of right angled triangle are in AP then the since of acute angle are

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Answer:

3/5 and 4/5

Step-by-step explanation:

sines are 3/5 and 4/5.

it is the rt. triangle with sides 3,4 and 5 .