The legs of a right triangle are 30 and 16. Find the hypotenuse.

From the condition, we know the lengths of the legs of a right-angled triangle are 30 and 16. We need to find the hypotenuse of a right-angled triangle.

To do this, we apply the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the legs.

a ^ 2 + b ^ 2 = c ^ 2;

It remains for us to substitute the known values and calculate.

30 ^ 2 + 16 ^ 2 = c ^ 2;

900 + 256 = c ^ 2;

c ^ 2 = 1156;

Let’s take the square root and get (we only need a positive value):

c = √1156 = √342;

c = 34.

Answer: The length of the hypotenuse is 34.