In a right triangle, the hypotenuse is 5 units long, and the legs also have integer lengths. How long are the legs?

Note: How many different cases are there?

In a right angled triangle, one angle is 90°.

Thus we can use pythagoras theorm to find the lengths of the sides of the triangle or if an angle is know then we can also find the lengths of the triangle by using trigonometric function like sin θ, cos θ and tan θ.

So, In this case we can use pythagoras theorm:

(Hypotenuse) ² = (height) ² + (base) ²

(5) ² = (h) ² + (b) ²

Here, since 2 side lengths are not know, the values are difficult to find.

If we consider trigonometric functions:

Since the angles are not known, it is difficult to find the other lengths.