Question
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
1) csc45degrees
2)sec30degrees
3)longest side of a 30-60-90
triangle if the side opposite the 60degree angle is 5radical3
Answers
Reiny
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
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