Question

In a right angle triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. (Class-IX)

Answer 1

The sum of the angles of a triangle is 180 degrees. When you take away 90 degrees you are left with 90 degrees. 

So the other angles are 30 degrees and 60 degrees. 

Since sin(30 degrees) = (1/2), and sin(x) = the length of the side opposite it divided by the length of the hypotenuse, then that side is (1/2) the size of the hypotenuse. That means that the hypotenuse is twice as long the side opposite the 30 degree angle.