9-1

This week we started Chapter 9. It is about using trigonometry to find unknown sides or angles of a right triangle. In Chapter 7, we defined the trigonometric functions in terms of coordinates of points on a circle. In this chapter, our emphasis shifts from circles to triangles. To solve right triangles, you must remember SOHCAHTOA which is:

sin theta = opp/hyp
cos theta = adj/hyp
tan theta = opp/adj

As we learned, cosecant, secant, and cotangent are all reciprocals:
csc theta = hyp/opp
sec theta = hyp/adj
cot theta = adj/opp

To solve right triangles, you also need to remember that hypotenuse is opposite of the right angle.
Here’s an example:
EXAMPLE 1: For triangle ABC, C=90 degrees, A=26 degrees, and a=38
A). Since we know angles A and C, let’s solve for B. Subtract 90 degrees and 26 degrees from 180 degrees to get your answer. Angle C = 64 degrees. Now we have all of our angles.
B). We are given angle A, so to solve for b and c use the functions above. To solve for c, use sin which is opp/hyp - sin 26 degrees = 38/c
C). Multiply both sides by c and continue solving - c = 86.684 degrees
D). Now that we have a and c, we need to solve for b. We will use tan which is opp/adj - tan 26 degrees = 38/b.
E). Multiply both sides by b and continue solving - b = 77.911 degrees

That’s it! You’ve solved the triangle. This section is simple if you know your formulas, draw your triangle, and insert your answers in it.