Question

A peer is having difficulty finding angle measures using trigonometric ratios in a right triangle. Create an example to demonstrate how to do this and be sure to address using the reciprocal relationships (cosecant, secant, cotangent too)

Answer 1

Please see diagram:
A right triangle has 3 main trigonometric ratios. These ratios are the relationships between different sides of the triangle, how large one side is compared to the other side. If you have every angle, in degrees, of a triangle, then you can figure out the relation between the lengths of the three sides. Additionally, you can figure out the value of the angles, given the sides of the triangle. 
In the diagram, we are interested in the trigonometric ratios with respect to angle a. 

You see in the diagram that sine, cosine, and tangeant are described as their ratios: (one way to remember: SohCahToa
sine = opposite / hypotenuse      
cosine = adjacent / hypotenuse                 
tangeant = opposite / adjacent. 

cosecant, secant, and cotangents are just the reciprocals of these ratios:
cosecant = 1 / sin 
secant = 1 / cosine
cotangeant = 1 / tangeant