Coming to the third example, we should have gained much more comfort and fluency with the process. While we're still doing a totally different problem, this should feel a lot like variations on a theme, which it is. You should begin to feel the method and see where the problem is going before you get there. Let's dive in.
Q: Calculate the opposite length based on the picture below.
1) Identify the right angle in your triangle. This confirms that you will be able to use the sohcahtoa rule.
See the square? Right triangle. Check.
2) Identify your angle of interest. This will change which sides are opposite and adjacent.
This is now the other angle compared with the last two problems. Let's see if this changes anything. Do you know yet?
3) Identify your opposite and adjacent legs of the triangle.
So a slight deviation from the past problems. Now we have the opposite and adjacent sides reversed. Notice how it can change from problem to problem? That's why we mark the sides. Don't forget to do yourself that service and avoid sloppy mistakes.
4) Using the sohcahtoa rule, set up a relationship using sin/cos/tan, the angle, and two of the adjacent/opposite/hypotenuse sides.
In this example, we actually know the angle, 53.14 DEGREES. When we go typing this in our calculator, remember to put the thing in degrees mode, or everything will be wrong. And, since we know the hypotenuse and angle, and are looking for OPPOSITE, we'll use sine, aka sin[theta] = opp/hyp = opp/5.
5) Solve the equation for your desired variable.
Multiply each side by 5 and we're done. The opposite side is 4. Big surprise?
6) Box your answer, you're done!
We're done! Is it going faster now? My comments have receded more and more through the examples. You should feel a lot more comfortable at this point. If there's anything confusing at this point, try going back through episode 35 and 36 again, as well as this past example. The more you go through it, the more you will absorb.
