In a right triangle the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=3, b=4;

The hypotenuse is 5

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse of a right triangle

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

3^2 + 4^2 = c^2

9+16=c^2

25=c^2

Take the square root of each side

sqrt (25) = sqrt (c^2)

5 = c

hypotenuse = 5

Step-by-step explanation:

Use the Pythagorean theorem:

a² + b² = c²

a, b - legs

c - hypotenuse

We have the lengths of the legs a = 3 and b = 4. Substitute:

c² = 3² + 4²

c² = 9 + 16

c² = 25 → c = √25

c = 5

Pythagorean triple:

3, 4, 5

6, 8, 10

5, 12, 13

and more.