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Exploring SOH CAH TOA 1. Draw a triangle on the CENTER of your grid paper using the dimensions on your card. Be sure to draw the picture like the following. C B x A 2. Find the length of the hypotenuse and label on your picture. (HINT: Use Pythagorean Theorem) 3. Using your protractor, measure angle x and label inside the triangle. Be as accurate as possible! 4. Fill in the table of ratios of lengths of the sides of the triangle: B A B C A C Fraction Form Decimal Form 5. Now look at your calculator. Change the mode to degree by pressing MODE and selecting DEGREE. 6. Look above the numbers. There are buttons labeled SIN, COS, and TAN. We are about use those! Yeah! 7. Fill in the table for angle x. Write answer as a decimal. For example, if you wanted to find sin (30), you would type SIN, 30, ENTER in your calculator! sin(x) cos(x) tan(x) 8. Now, match up the side ratios from the first chart with the corresponding trig expression (sin, cos, or tan). sin(x) = _____________ cos(x) = ________________ tan(x) = ________________ 9. Compare with your partner. Did you guys get the same matches? If not, someone made a mistake someone! Please fix it! 10. So, if we labeled a triangle as shown, fill in the following general formulas (with words instead of letters). Hypotenuse (C) Opposite (B) cos(x) x Adjacent (A) sin = cos = sin(x) tan(x) tan= Let’s practice some problems! Find tan A and tan B. Write each answer as a decimal rounded to four decimal places. 1. 2. tan A________ tan A ________ tan B ________ tan B ________ Find the sine and cosine ratios. 3. sin z =______ cos z =______ sin x =______ cos x =________ 82 18 z 80 4. x 18 82 80 Find the value of x to the nearest tenth. 5. x = __________ 6. x = _______ Use a sine or cosine ratio to find the value of each variable. 7. . 26 8. 30 x 18 y x 32 y x = ___________ x = ___________ y = ___________ y = ___________ Draw a right triangle with the following: Draw a right triangle with the following: Draw a right triangle with the following: Leg length = 10 units Leg length = 24 units Leg length = 10 units Leg length = 24 units Leg length = 10 units Leg length = 24 units Draw a right triangle with the following: Draw a right triangle with the following: Draw a right triangle with the following: Leg length = 5 units Leg length = 12 units Leg length = 5 units Leg length = 12 units Leg length = 5 units Leg length = 12 units Draw a right triangle with the following: Draw a right triangle with the following: Draw a right triangle with the following: Leg length = 8 units Leg length = 15 units Leg length = 8 units Leg length = 15 units Leg length = 8 units Leg length = 15 units Draw a right triangle with the following: Draw a right triangle with the following: Draw a right triangle with the following: Leg length = 3 units Leg length = 4 units Leg length = 3 units Leg length = 4 units Leg length = 3 units Leg length = 4 units Draw a right triangle with the following: Draw a right triangle with the following: Draw a right triangle with the following: Leg length = 9 units Leg length = 12 units Leg length = 9 units Leg length = 12 units Leg length = 9 units Leg length = 12 units Draw a right triangle with the following: Draw a right triangle with the following: Draw a right triangle with the following: Leg length = 6 units Leg length = 8 units Leg length = 6 units Leg length = 8 units Leg length = 6 units Leg length = 8 units