Final answer:
Using the Pythagorean theorem, the hypotenuse of a right triangle with legs measuring 6 cm and 15 cm is found to be approximately 16.1 cm when rounded to the nearest tenth.
Step-by-step explanation:
To find the measure of the hypotenuse of a right triangle when given the lengths of both legs, we use the Pythagorean theorem. This 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 expressed as:
a² + b² = c².
For the given triangle with legs measuring 6 cm (a) and 15 cm (b), we calculate the length of the hypotenuse (c) as follows:
c = √(a² + b²)
c = √(6² + 15²)
c = √(36 + 225)
c = √261
c ≈ 16.1 cm
Hence, the hypotenuse measures approximately 16.1 cm when rounded to the nearest tenth.