We are given a right triangle with one leg and the hypotenuse. Our task is to find the length of the other leg.
Given:
- One leg ([tex]\( a \)[/tex]) = 3
- Hypotenuse ([tex]\( c \)[/tex]) = [tex]\( \sqrt{34} \)[/tex]
We will use the Pythagorean theorem to find the other leg ([tex]\( b \)[/tex]). According to the Pythagorean theorem:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Substitute the known values into the equation:
[tex]\[ 3^2 + b^2 = (\sqrt{34})^2 \][/tex]
Simplify the equation:
[tex]\[ 9 + b^2 = 34 \][/tex]
To solve for [tex]\( b^2 \)[/tex], subtract 9 from both sides:
[tex]\[ b^2 = 34 - 9 \][/tex]
[tex]\[ b^2 = 25 \][/tex]
Now, take the square root of both sides to solve for [tex]\( b \)[/tex]:
[tex]\[ b = \sqrt{25} \][/tex]
[tex]\[ b = 5 \][/tex]
Therefore, the length of the other leg is 5.
Now, let's identify the correct answer from the given options:
A. 8
B. 34
C. 5
D. [tex]\( \sqrt{43} \)[/tex]
The correct option is C. 5.
