One of the legs of a right-angled triangle is 4, and the hypotenuse is 5. Find the other leg of this triangle.

From the condition it is known that one of the legs of a right-angled triangle is 4, and the hypotenuse is 5. And we need to find the second leg of this triangle.

Let’s apply the Pythagorean theorem for this. Let’s remember her.

The square of the hypotenuse is equal to the sum of the squares of the legs. Let’s write the Pythagorean theorem like this:

c ^ 2 = a ^ 2 + b ^ 2.

Let us express the length of one of the legs from the formula:

a ^ 2 = c ^ 2 – b ^ 2;

a = √ (c ^ 2 – b ^ 2).

it remains to substitute the values into the formula and perform calculations:

a = √ (5 ^ 2 – 4 ^ 2) = √ (25 – 16) = √9 = 3.

Answer: the second leg is 3.