Questions: Find the length of the unknown side of the triangle. The length of the unknown side of the triangle is . (Simplify your answer. Type an exact answer, using radicals as needed.)

Solution Steps

The given triangle is a right triangle, as indicated by the right-angle symbol.

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

In this problem, the lengths of the two sides are given as 4 m and 5 m. We need to find the length of the hypotenuse (c). \[ c^2 = 4^2 + 5^2 \] \[ c^2 = 16 + 25 \] \[ c^2 = 41 \]

To find the length of the hypotenuse, take the square root of both sides: \[ c = \sqrt{41} \]

Final Answer