Ex.) On the Green (1st, 3rd Per) or Orange (2nd Per) Trigonometry Practice Worksheet, for problem #1, we were asked to find the “sin A“. We should have gotten 27/45. Originally we stopped there. If we actually do the division of 27/45 though, we get .6. So now we know that “sin A“, whatever A is, must equal .6. sin A = .6
If you look in the sine column on your blue table of trig values, you should be able to find a number very close to .6 (it should be .6018). You should be able to see that this means the sin(37º)=.6018, so in for #1 on this worksheet, <A must equal about 37º. This is inverse trigonometry!
Using this idea, we solved for the unknown angles of problems 2-4, and then on the back, 15-18.
We then worked through this sheet of Triangle Word Problems: Mixed Triangle Word Problems
The key to this problem is making accurate diagrams. All triangle diagrams have some sort of horizontal side, a height (vertical), and a hypotenuse (the horizontal side and height meet at a right angle, making the 3rd side the hypotenuse).
You need to use your knowledge of the English language, to determine what makes sense to go where. When we talk about a person being 6 ft tall, that’s going to be on the vertical side (height) of your triangle. When we talk about the length of a shadow, since shadows exist on the ground, that will be the horizontal, bottom, part of your triangle.
If we talk about a person standing 20 feet away from something else, that distance is measured on the ground (Not through the air, or up and down!).
So label what is described on a triangle, and use trigonometry, or similarity, or special right triangles to solve for unknown sides or angles.