Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
THE TANGENT RATIO UNIT 10: SECTION 8.5 OBJECTI VE: TO DEFI NE THE TANGENT RATI O FOR AN ACUTE TRI ANGLE. TO SOLVE RI GHT TRI ANGLE PROBLEMS USI NG THE TANGENT RATI O. TRIGONOMETRY Trignometry – comes from the Greek words that mean “triangle measurement. Our Study will be limited to the trigonometry of Right Triangle. Purpose (video link) : Introduce the very important ratio, called the tangent ratio, that is formed by using the lengths of the legs of a right triangle. BUT FIRST – EVERYONE NEEDS A CALCULATOR Find the tangent, sine, and cosine keys on the calculator. Example 1: Use a calculator to find the value of each to the nearest ten-thousandth. 1) sin 21° 2) tan 22° Practice 1: Use a calculator to find the value of each to the nearest ten-thousandth. 1) cos 20° 2) sin 77° 3) tan 17° 4) cos 87° Find the inverse tangent, sine, and cosine keys on the calculator. cos 1 tan 1 sin 1 Example 2: Find each angle measure to the nearest degree. 1) sin B = 0.4848 2) cos W = 0.6157 3) tan W = 19.0811 Practice 2: Find each angle measure to the nearest degree. 1) sin A = 0.5150 2) cos A = 0.7431 3) cos A = 0.5878 4) cos A = 0.4226 5) tan W = 0.5317 6) sin A = 0.7431 1) tan 24° = _________ 2) tan 41° = _________ 3) tan 88° = _________ 4) tan ______ = 2.4751 5) tan ______ = 0.3057 6) tan ______ = 0.8098 Extra Practice: NOW INTRODUCING THE TANGENT RATIO Tangent ∠x = Side Opposite ∠x Side Adjacent ∠x Tangent ∠x = Side Opposite ∠x Side Adjacent ∠x Side Adjacent ∠x x Side Opposite ∠x Practice 70° 29.24 10 90° 20° 27.47 Using the given triangle, find the following measures to the nearest hundredth. 1) leg opposite 20° leg adjacent 20° 2) tangent 20° 3) leg opposite 70° leg adjacent 70° 4) tangent 70° USING THE TANGENT RATIO Use the tan proportion to solve the following. Example 3 x 37° 12 13.5 80° x Guided Practice: Find tan A, tan B, m∠A, and m∠B 1. C 7 A 2 A B 2. 17 B 3. Find the value of x to the nearest tenth. 15 8 20 24° x C Guided Practice: Find the value of x to the nearest tenth 10 4. 35° x Find y° correct to the nearest degree. 8 5. 5 y° 6. 8 6 y° 10 Closure: 1. What the name of the branch of mathematics that uses tangents, cosines, and sines? 2. State the tangent ratio. Homework: P308 Written Exercises: #1-18a