Final answer:
The Pythagorean theorem can be used to find the value of c in a right triangle when given the lengths of the other two sides. By substituting the given values of a and b into the theorem and solving for c, we can find the answer.
Step-by-step explanation:
The Pythagorean theorem relates the lengths of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by: a² + b² = c². To find the value of c, substitute the given values of a and b into the equation and solve for c.
Given a = 4 and b = 14, we have: 4² + 14² = c². This simplifies to 16 + 196 = c², and further simplifies to 212 = c². Taking the square root of both sides, we get c = √212, which is approximately 14.6.
Rounded to the nearest tenth, c is approximately 15.6. Therefore, the correct answer is option c) 15.6.