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Section 10.4 and 10.5: Sine-Cosine-Tangent Opposite/Adjacent/Hypotenuse To understand sine, cosine, and tangent, you must be able to find label sides as adjacent or opposite of an angle. What side is the hypotenuse? B c a C What side is opposite of A? What side is adjacent to A? What side is opposite of B? What side is adjacent to B? A b Sine (sin) The sine (or shorthand sin) is simply a ratio in a right triangle comparing the side opposite an angle to the hypotenuse. For example, sin 40 64 100 16 25 Sine (sin) / Cosine(cos) / Tangent(tan) To remember the trigonometric ratio we can use the following saying: Sin = _________ Cos = _________ Tan = _________ Using the triangle below express sine-cosine-tangent. B 5 3 C 4 sin A = -------- sin B = ------- cos A = ------- cos B = ------- tan A = ------- tan B = ------- A Examples: Use the triangle below to find sin, cos, tan. NO DECIMALS! 1. sin A = 2. cos A = 3. tan A = 4. sin B = B C 7 25 A 5. cos B = 6. tan B = Finding Missing Sides You can find trigonometric ratios using your calculator! **** Make sure your calculator is in _________________**** Examples: Find the values using your calculator 7. sin 45o 8. cos 87o 9. tan 37o Examples: Find the missing side lengths. 10. 11. B X 12. 13. A 34 10 Y C 15. A 15-foot ladder leans against a wall. The angle of elevation (the angle between the ladder and ground) is 70o. How far up the wall does the ladder reach?