2/23/16- Triangle Word Problems and Inverse Trigonometry

Warm-Up

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We then reviewed Inverse Trigonometry. Inverse Trig is basically the process of working backwards on our Blue Trig tables to find unknown angles.

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.

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