Final answer:
To find the height of a tower, the Pythagorean theorem or trigonometry can be used depending on the available information. The Pythagorean theorem applies if two sides of a right triangle are known, while trigonometry is used if an angle and one side are known. Calculus integration and Archimedes' principle are not suitable for this problem.
Step-by-step explanation:
To find the height of a tower based on given information, we can apply different mathematical principles. One common method is using the Pythagorean theorem which 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).
Thus, if we are given the lengths of these sides, we can find the hypotenuse or one of the legs by rearranging the theorem: c = √(a² + b²) or a = √(c² - b²). If the tower forms one side of a right triangle, we can use this to calculate its height.
Another method involves trigonometry, which can be used if we know an angle and one side of a right triangle. The height (h) can be found using trigonometric functions such as sine, cosine, or tangent. For example, if the base of the tower and angle are known, we can use tangent: tan(angle) = h / base, and solve for h.
If the conditions are suitable, we could also use calculus integration, such as when we need to find the area under a curve or if the height changes with respect to another variable. However, without a specific function or curve, we cannot apply integration here. Similarly, Archimedes' principle is not applicable in calculating the height of a tower, as it's a principle related to fluid mechanics.
Therefore answer is b. Pythagorean theorem.