No, only your brain can. Similar triangles can be used to solve some problems but not others but it is for you to work out - using your brain - whether or not similar triangles are relevant and then to figure out how they might be used.
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Yes, the sine, cosine and tangent are integral to problem solving (angles and side lengths) in right angle triangles (triangles with a 90 degree angle included).
For solving the properties of triangles
By finding a pattern the first time you solve a problem, then applying this pattern (algorithm) to solve similar problems.
Describe how you exhibit effective problem solving skills?
Defining the problem.