Questions: Find the exact length of the third side of the triangle using the Pythagorean th

Solution Steps

The problem provides the lengths of two sides of a right triangle:

• One leg (a): 5 cm
• Hypotenuse (c): 19 cm

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): \[ c^2 = a^2 + b^2 \]

Substitute the given values into the Pythagorean theorem: \[ 19^2 = 5^2 + b^2 \] \[ 361 = 25 + b^2 \]

Isolate \( b^2 \) by subtracting 25 from both sides: \[ 361 - 25 = b^2 \] \[ 336 = b^2 \]

To find \( b \), take the square root of both sides: \[ b = \sqrt{336} \] \[ b = \sqrt{16 \times 21} \] \[ b = 4\sqrt{21} \]

Final Answer