Jan 1 4:08 PM. We write this in a shorter manner for simplicity. leg

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1 Review Pythagorean Theorem Jan 1 4:08 PM We write this in a shorter manner for simplicity. leg hyp leg or a c b Note, the last statement can be misleading if the letters used are not in the correct position. Be careful. Jan 1 4:04 PM 1

2 Find the missing side length (draw the squares on each side if necessary) 6 h 8 Sep 23 9:18 AM Find the missing side length (draw the squares on each side if necessary) a Sep 23 9:18 AM 2

3 Find the missing angle in the following triangles: a 24 o 46 o a a May 29 11:55 AM Trigonometry primary trigonometric ratios Learning Goal: By the end of today, we will be able to solve for missing sides and angles in right triangles using the primary trigonometric ratios (SohCahToa). May 27 8:26 AM 3

4 Background Information On the graph paper provided, draw a right triangle, ΔABC, with the following dimensions, 3,4,5. Fill in the ratios of side lengths for ΔABC, use both fraction and decimal form: 5 C 3 A 4 B Using a protractor, measure the angles at A and C May 25 11:27 AM I very kind person created something called the trigonometry tables. They determined that there is an angle attached to every ratio of sides. If the ratio of the sides is 0.5, then that coincides with an angle of 30 o. The problem was making sure that we were all talking about the SAME ratio of sides. The primary trigonometric ratios were born. By giving names to the ratios we were talking about ensured that everyone was on the same page. Sine Cosine Tangent Soh Cah Toa opp hyp desired angle adj θ May 27 11:38 AM 4

5 Soh Cah Toa The entire preceding table is also stored in your calculator. Jan 6 10:56 AM Calculators have mini Trig tables stored inside of them (sorta). sin, cos, tan Angle TO ratio (a) sin (35 o ) = ANGLERATIO (b) cos (45 o ) = (c) tan (78 o ) = sin 1, cos 1, tan 1 (arcsine, arccosine,arctan) second function/shift sin,cos,tan May 28 11:48 AM 5

6 What is the RATIO that goes with following trigonometric ratio? sin(80 o ) = R R = Use the table and your calculator to verify. cos (12 o ) = R R = tan(55 o ) = R R = May 27 12:07 PM Solve for "x" (use your trig table or calculator) May 27 12:06 PM 6

7 Solve for "x" (use your trig table or calculator) May 27 12:06 PM Choose the most appropriate Trig Ratio, and use it to find the missing "y" value. y o May 27 12:47 PM 7

8 Calculators have mini Trig tables stored inside of them (sorta). sin, cos, tan Ratio TO Angle (a) sin (A) = 0.68 ANGLE RATIO (b) cos (B) = sin 1, cos 1, tan 1 (arcsine, arccosine,arctan) second function/shift sin,cos,tan (c) tan (K) = May 28 11:48 AM What is the ANGLE (A) that goes with following trigonometric ratio? sin(a) = 0.67A = cos (A) = 0.76 A = tan(a) = 1.3 A = May 27 12:07 PM 8

9 Find the angle that corresponds with the given ratio. (a) (b) (c) May 28 11:56 AM Choose the most appropriate Trig Ratio, and use it to find the missing "A" value. 5 8 A May 27 12:47 PM 9

10 Find the missing value in the triangle below: Checklist Is the triangle a RIGHT triangle? What trig ratio ties the information together (sin, cos, tan)? Am I looking for an angle or a ratio (side)? A o May 28 11:40 AM Choose the most appropriate Trig Ratio, and use it to find the missing "y" value. 48 o y 16 May 27 12:47 PM 10

11 Find the missing value in the triangle below: Checklist Is the triangle a RIGHT triangle? What trig ratio ties the information together (sin, cos, tan)? Am I looking for an angle or a ratio (side)? A o May 28 11:40 AM Consolidation Questions: Page #1 5, 8, 10 May 27 12:50 PM 11

12 page #1, 2, 3,5, 7, 9, 11 horizontal or reference line angle of elevation angle of depression horizontal or reference line Jan 10 9:27 AM 12