To find the length of the hypotenuse in a right triangle when the lengths of the other two sides are given, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse [tex]\( c \)[/tex] is equal to the sum of the squares of the other two sides [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. The formula is:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Given:
- The length of one leg [tex]\( a \)[/tex] is 3.
- The length of the other leg [tex]\( b \)[/tex] is 4.
Now, follow these steps:
1. Square the lengths of the legs:
[tex]\[ a^2 = 3^2 = 9 \][/tex]
[tex]\[ b^2 = 4^2 = 16 \][/tex]
2. Add the squares of the legs:
[tex]\[ a^2 + b^2 = 9 + 16 = 25 \][/tex]
3. Take the square root of the sum to find the hypotenuse [tex]\( c \)[/tex]:
[tex]\[ c = \sqrt{25} = 5 \][/tex]
Therefore, the length of the hypotenuse is:
[tex]\[ 5.0 \][/tex]
So, if the legs of a right triangle are 3 and 4, the length of the hypotenuse is 5.
