In a right triangle, if one leg has length $3$ units, the other leg has length $4$ units, and angle $b$ is opposite the side of unknown length, what is the length of the side opposite angle $b$?

• A. $4$ units
• B. $5$ units
• C. $6$ units
• D. $3$ units

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle: the two legs are given as 3 units and 4 units, and the hypotenuse is the side opposite the right angle, which is unknown here.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two legs. This can be written as: \(c^2 = a^2 + b^2\) where \(c\) is the hypotenuse.
3. Since angle \(b\) is opposite the side of unknown length, and the two legs are 3 and 4 units, determine which side corresponds to angle \(b\). If angle \(b\) is opposite one of the legs, then that leg's length is the side opposite angle \(b\).
4. If angle \(b\) is opposite the leg of length 4 units, then the length of the side opposite angle \(b\) is 4 units. If angle \(b\) is opposite the hypotenuse, use the Pythagorean theorem to find the hypotenuse: calculate \(c = \sqrt{3^2 + 4^2}\).
5. Calculate the square root to find the length of the hypotenuse, which will give the length of the side opposite angle \(b\) if it is the hypotenuse. This completes the process to find the side length opposite angle \(b\).