A right angle triangle has three sides and three interior angles one of which is 90 degrees. The names of its sides are the adjacent the opposite and the hypotenuse and using the 3 trig ratios we can find the interior angles or lengths of the sides depending on the information given.
Tangent angle = opposite/adjacent
Sine angle = opposite/hypotenuse
Cosine angle = adjacent/hypotenuse
If we are given the lengths of 2 sides we can work out the angles with the above ratios.
If we are given a length and an angle we can work out the lengths of the other 2 sides by rearranging the above ratios.
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It allows the ratios to be compared more easily. But they are NOT all defined as unit ratios. My monitor has an aspect ratios of 4:3 or 16:9.
You do not solve ratios: they are simply a form of numbers. There may be questions whose solutions require you to work with ratios but there the answer will depend on the sort of question you have to deal with.
Ratios that are equal to each other can be 3/4=75/100 or 1/4=25/100
They are both trig values, but not equal. Tan 45 is 1 and sin 45 is 0.7071