Finish Calculating Ratios from last Friday Warm UP: Find x: 1. x 2. L ║ M 3. Read and highlight “Trigonometry” 22April 2013 Geometry 144º 7 6 x 5 L M

Objective Students will use trig ratios to find missing side lengths in triangles. Students will take notes and work with their group. ACT Testing on April 23- ONLY JUNIORS come to school HOMEWORK DUE TUESDAY midnight Spring Project Proposal DUE Wed/ Thursday “Why did the mural painter…” both sides

Right Triangle Vocabulary hypotenuse- the longest side leg adjacent- “next to” leg opposite- “across” Hypotenuse ANGLE Adjacent Opposite

Activity-Calculating ratios for similar triangles EXPECTATIONS- Take 5 minutes to finish 1. Complete the worksheet writing the ratios as a fraction and decimal for your two triangles. each person filling in their DECIMAL COLUMN for all triangles measuring. 2. Share your results with your group- each person filling in their DECIMAL COLUMN for all triangles measuring. the mean values for each ratio rounding to 2 decimal places. 3. Calculate the mean values for each ratio rounding to 2 decimal places.

on a calculator 1. MAKE SURE YOU ARE IN DEGREE MODE mode  arrow to DEGREE  enter  2 nd QUIT 2. Try it on your calculator for YOUR angle measure: sin 45⁰sin 30⁰sin 60⁰sin 20⁰ cos 45⁰cos 30⁰cos 60⁰cos 20⁰ tan 45⁰tan 45⁰tan 60⁰tan 20⁰ WHAT DO YOU NOTICE?

sine, cosine and tangent with the same acute angle measuresimilar these ratios are PROPORTIONAL and their decimals are equivalent, NO MATTER THE SIDE LENGTHS the trig functions sine, cosine and tangent are RATIOS of side lengths of right triangles Since right triangles with the same acute angle measure are similar (AA Similarity Conjecture) these ratios are PROPORTIONAL and their decimals are equivalent, NO MATTER THE SIDE LENGTHS

SOH CAH TOA Sine, Cosine and Tangent are special ratios defined as follows: SOH CAH TOA Sine = “sin” ϴ = Cosine = “cos” ϴ = Tangent = “tan” ϴ = MEMORIZE THESE!! WRITE THESE DOWN

SKETCH on your paper MARK sides H, A and O Find the ratios: sin A = cos A = tan A = sin B = cos B = tan B = What do you notice? Any patterns? A B

Read Trigonometry Handout HIGHLIGHT / underline or circle key phrases: 1) What does Trig mean? 2) What do we call angle “x”? 3) What happens to adjacent and opposite if the angle changes position? 4) Adjacent means __________ Opposite means ___________ 5) MEMORIZE how? 6) How do you know which ratio to use?

solving equations with trig functions 1) Strategy– rewrite the trig function as a decimal and solve for the unknown value ex:  sin 42⁰ ≈ = 20 (0.6691) = x x =

solving equations with trig functions 2)– remember sinϴ, cosϴ, tanϴ are RATIOS YOU CAN NOT DIVIDE the angle measure to simplify!!! use parenthesis STRATEGY– use parenthesis to help you remember! 20 (sin 42⁰) = x multiply both sides by (0.6691) = x use calculator x =

How do you know which trig ratio you need to use to help find “x”? 1) use SOH CAH TOA 2) LABEL H, A and O on your triangle. 3) WHAT information DO YOU KNOW? 4) WHAT DO YOU NEED TO FIND? SOH CAH TOA

practice HOW do you know which function to use? LABEL H, A and O WHAT INFORMATION do you KNOW? WHAT DO YOU NEED TO FIND? Choose the trig function that incorporates those values!! COMPLETE HANDOUT- TRIGONOMETRY first section # Set up and solve for the unknown value.

debrief Why do the trig ratios remain equivalent for any acute angle, no matter how big the triangle? How do you know which trig function to use when solving trig problems?