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Download Teaching the Ratios Lesson 1 (editable)
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Right Triangle Ratios 1. In the following triangles, find the length of the hypotenuse. x 4 ft. x 12 in. 36˚ 7 in. 2. How many side lengths of the right triangle must you know to be able use the Pythagorean Theorem? 3. Trigonometry is what you use when you can’t use the Pythagorean Thm. Here is what you need to know to use Trig. a. One acute angle measure b. One side of the right triangle 4. Trigonometry is based on ratios. The ratios are developed by comparing sides of the right triangle based on their location compared to the acute angle. Look at the illustration below. Example 2 Hypotenuse 38˚ Hypotenuse Adjacent Leg Opposite Leg Example 1 38˚ Opposite Leg Adjacent Leg Look at the right triangle below and finish completing the ratios by filling in the missing numbers Adjacent Leg = 12 = 3 Hypotenuse 20 5 Opposite Leg = ____ = _____ Hypotenuse 20 20 ft 16 ft Opposite Leg = _____ = ______ Adjacent Leg 24˚ 12 ft Complete the ratios for the given triangles using the given angle, α (Theta). Some of these triangles are similar. As you complete the trigonometry ratios, decide which triangles are similar and list them in the table on the following page. Not drawn to scale H D C 13 5 4√5 12 α 16 α 8 α A P T. 8 O 12 O G 8√3 Opp. Leg = ______ Opp. Leg = ______ Opp. Leg = ______ Hypotenuse Hypotenuse Hypotenuse Adj. Leg Hypotenuse = ______ Adj. Leg Hypotenuse = ______ Adj. Leg Hypotenuse = ______ Opp. Leg Adj. Leg = ______ Opp. Leg Adj. Leg = ______ Opp. Leg Adj. Leg = ______ N B B 48 24 α 4 α T 9 α E 24√ 3 26 10 T Opp. Leg Hypotenuse = ______ Adj. Leg Hypotenuse = ______ Opp. Leg Adj. Leg = ______ D A 8 Opp. Leg Hypotenuse I 24 = ______ Opp. Leg = ______ Hypotenuse Adj. Leg Hypotenuse = ______ Adj. Leg Hypotenuse = ______ Opp. Leg Adj. Leg = ______ Opp. Leg Adj. Leg = ______ W L C α 12 N α √985 29 √410 11 8 18 A G O 17 Y α 16 Opp. Leg Hypotenuse = ______ Opp. Leg Hypotenuse = ______ Opp. Leg = ______ Hypotenuse Adj. Leg Hypotenuse = ______ Adj. Leg Hypotenuse = ______ Adj. Leg Hypotenuse = ______ Opp. Leg Adj. Leg = ______ Opp. Leg Adj. Leg = ______ Opp. Leg Adj. Leg = ______ H Write the names of the similar triangles, using the vertices, from the previous page in the table below Triangle 1 Example CAT is similar ~ Triangle 2 DOG 5. These ratios have special names that match several keys on your calculator Sine Ratio (SIN) is Opposite Leg (of acute angle) Hypotenuse Cosine Ratio (COS) is Adjacent Leg (to acute angle) Hypotenuse Tangent Ratio (TAN) is Opposite Leg Adjacent Leg 6. One mnemonic device for helping you remember these ratios is SOHCAHTOA SinOppHypCosAdjHypTanOppAdj 7. The Sin, Cos, Tan ratios are always in relation to one of the acute angles of the right triangle – thus you find the relationships, opposite leg of the acute angle or adjacent leg to the acute angle. Everything is in relation to the acute angle.
