how are the concepts of similar figures and trigonometry used in real life?

Answer 1

Mostly, they aren't. Outside my field of engineering, I have only used geometry and trig on about 2 occasions in 25 years. In both cases, I could have gotten by without it.

Within my field, I use them quite often. So I suppose it depends on what you end up doing for a living as to whether or not you will really use this stuff. But it's better to be prepared than to be incapable.

Answer 2

Any scale model involves similarity, because similar figures are the same size, but different shapes from real world objects. Maps and photographs are also good examples of similarity, because they preserve original shapes in a specific ratio.

One use of trigonometry is in finding measures of objects that can't be easily accessed. Classic story problems about finding the heights of trees, flagpoles, and buildings are all based on this. Surveying uses trigonometry by measuring distances (normally with lasers) from different angles, and the global posititoning system is basically a more complex version of the same idea.