Let's see how to apply trigonometry to working in triangles which do not contain a right angle.
The ratios of each side to the sine of its "partner" are equal to each other.
These ratios, in pairs, are applied
to solving problems. You never need to use all three ratios at the same time.
Mix and match the ratios to correspond with the letters you need.
Remember when working with proportions, the product of the means
equals the product of the extremes (cross multiply).
Example 1: In , side a = 8, m<A = 30º and m<C = 55º. Find side c to the nearest tenth of an integer.
If the problem asks to find a missing angle, there is another step required for the solution.
Example 4: In the diagram, a = 55, c = 20, and m<A = 110º. Find the measure of <C to the nearest degree.
Unfortunately, this is NOT the answer!!
(Since triangle ABC already has an obtuse angle of 110 degrees, we can eliminate the notion that sin is also positioned in Quadrant II, which would give us a second obtuse angle.