HONORS GEOMETRY 8.4. Trigonometry Day One

Do Now: Find all missing sides

Homework Questions? Comments? Confusions? Concerns?

Example One: Name the side or angle… Name the angle opposite RE. Name the side opposite ∠ R. Name the sides adjacent to ∠ Q. Name the angle opposite QR.

You Try! Given the right triangle TYL below, Name the side opposite the right angle. Name the angle opposite YL. Name the side adjacent to ∠ T that is not the hypotenuse. Name the angle opposite YT.

What happens?

Turns out! That every single right triangle in the world has a pattern for the sides just like the and the BUT, how can we realistically learn them all when there are so many possibilities? This is where trigonometry comes in :D

Sine Ratio: In a right triangle with acute <A, the sine of <A (written sin A) is the ratio of the length of the leg opposite <A to the length of the hypotenuse.

Cosine Ratio: In a right triangle with acute <A, the cosine of <A (written cos A) is the ratio of the length of the leg adjacent to <A to the length of the hypotenuse.

Tangent Ratio: In a right triangle with acute <A, the tangent of <A (written tan A) is the ratio of the length of the leg opposite <A to the length of the leg adjacent to <A.

Realize: Sine, Cosine and Tangent give you your relationships/the pattern so we don’t have to memorize them all! Also realize: The hypotenuse will NEVER be the adjacent or opposite side. It will always be the hypotenuse You need a RIGHT triangle to use ANY of these relationships. You can not take the sine/cosine/tangent of a 90 degree angle!

Helpful Mnemonic: SOH – CAH – TOA

Example Two: Find Sin L, Cos L, Tan L Find Sin N, Cos N, Tan N

Example Three: Find Sin D, Cos D, Tan D, Sin G, Cos G, Tan G.

You Try! Find Sin, Cos, and Tangent of C, A, T and C.

Example Four: Find QR and PR to the nearest tenth of a meter

On a Calculator Hit MODE (next to the 2 nd button) In the third row make sure DEGREE is highlighted and not RADIAN. If radian is, use the arrows to scroll down and over until DEGREE is highlighted and then click enter. Sin, Cos, Tan buttons are all on the calculator! Just hit sin then enter the angle and close parentheses and you can solve for the answers to problems!

Example Five: Find the missing sides

Example Six: Find AB and AC

You Try! Find all missing sides

Example Seven: Find x.

Example Eight: Find CD

Example Nine Find all missing sides

Example Ten: Find x

You Try! Find b and x.

Example Eleven: EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor?

You Try! CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, about how high does the ramp rise off the ground to the nearest inch?

Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me and your peers a question if you are confused!

Exit Ticket: Find x.