How angles was calculated

Question

In the past, how did they calculate the angles and sides of a right angle triangle without using a calculator?

Answer 1

The short answer is: they didn’t.

To calculate something, you need a calculator or a computer. Before electronic calculators there were mechanical calculators, and before that, computers were people with pencil and paper (or other means of recording the steps of their computations).

Seriously, “computer” used to be a job title under which numerous people were employed.

In the days when all computers were people, however, people rarely calculated trigonometric functions. Instead, most people who needed these results looked them up in books of trigonometric tables. It was far more efficient to have a relatively small number of computers work out all the data required to fill these tables and then to publish and distribute the books rather than have everyone who needed a sine or tangent have to calculate it themselves.

When two or three digits of accuracy was enough, devices such as slide rules could also be used. Again, this meant a relatively small number of people actually had to calculate where the marks on slide rules needed to be placed, and everyone else just used those markings to work with trigonometric functions.