Looks like you have several questions of this type.
At the top of your notebook, draw two triangles
the 45-45-90 and the 30-60-90 triangle with their sides.
Without any further work you can now find the 6 trig ratios of 30° , 45°, and 60°
1) and 2) become trivial after that
e.g. csc 45° = 1/sin45° = 1/ (1/√2) = √2
3) set up a ratio between your triangle and the basic 30-60-90 triangle, that is, ....
x/2 = 5√3/√3
x/2 = 5
x = 10
Or by the "just look at it" concept, ....
notice that your side is 5 times as big as the basic side, so your longest side must be 5 times the hypotenuse of the basic triangle. 5x2 = 10
Use the special triangles to find the exact values of the following:
1) csc45degrees
2)sec30degrees
3)longest side of a 30-60-90
triangle if the side opposite the 60degree angle is 5radical3
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