TRIGONOMETRY Objective: To use the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle.

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Presentation transcript:

TRIGONOMETRY Objective: To use the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle.

RISE AND SHINE, MATHLETES! AGENDA 1. HOMEWORK CHECK 2. NOTES – INTRO TO TRIG 3. PRACTICE HOMEWORK FINISH TRIG WORKSHEET

WHAT IS “TRIGONOMETRY”? Trigonometry deals with triangles. The word trigonometry actually comes from the Greek words trigon meaning—no big surprise here—triangle, and metron meaning something like “measure.” Trigonometry is all about figuring out clever ways to measure and calculate the properties of the components of triangles—namely their three sides and three angles.

IN A RIGHT TRIANGLE… There are ratios we can use to determine side lengths. These ratios are constant, no matter what the lengths for the sides of the triangle are. These ratios are called trigonometric ratios. Three of the trigonometric ratios are: Sine (sin) Cosine (cos) Tangent (tan)

SOHCAHTOA

TRIG RATIOS leg opposite of angle leg adjacent to angle opposite leg adjacent leg hypotenuse = = =

1. WRITE THE TRIG RATIO FOR THE FOLLOWING:

2. USE THE TRIANGLE TO WRITE EACH TRIG RATIO.

HAVING TROUBLE WITH DECIDING WHAT IS “OPPOSITE” VS. “ADJACENT?

3. USE THE TRIANGLE TO WRITE EACH TRIG RATIO

IF GIVEN THE ANGLE MEASURE, YOU CAN USE A TRIG FUNCTION TO FIND A MISSING SIDE LENGTH OF A RIGHT TRIANGLE Which trig ratio relates the given angle, and the 2 sides? Set up equation:

5. FIND X.

6. FIND X.

WORD PROBLEMS 7. To measure the height of a tree, Noah walked 125 ft. from the tree, and measured a 32˚angle from the ground to the top of the tree. Estimate the height of the tree. Draw a picture.

WORD PROBLEMS 8. A 20 ft wire supporting a flagpole forms a 35˚ angle with the flagpole. To the nearest foot, how high is the flagpole? Draw a picture.