Final answer:
Trigonometry is used in construction, navigation, and engineering to calculate precise measurements and is considered highly reliable due to its consistent logic based on mathematical postulates. Correct option is A) Construction, navigation, engineering.
Step-by-step explanation:
The formula of trigonometry is applied in various real-life situations, especially in A) Construction, navigation, engineering. These fields often require precise measurements and calculations to ensure the safety, functionality, and efficiency of structures, pathways, and devices. For example, in construction, trigonometry is used to determine the heights of buildings, depths of foundations, and angles of support structures. In navigation, it helps in charting courses and determining the position of a ship or an aircraft relative to its destination. Engineering utilizes trigonometry in numerous aspects, from designing mechanical components to analyzing the forces within structures.
It is also important to note that trigonometry is a reliable mathematical tool. This reliability stems from the fact that it is based on a set of postulates, which guarantees that every calculation flows logically from the previous ones, similar to how theories in physics are verified through experiments.
A graphical method such as drawing vectors to scale can be useful for a visual approximation in navigation, but using analytical methods with trigonometry can provide more accurate results because it involves detailed calculations rather than estimations made from a graph.