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The Tangent Ratio CHAPTER 7 RIGHT TRIANGLE TRIGONOMETRY

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You will need a protractor for this activity 1. Each person draw a right triangle ( ∆ ABC) where ﮮ A has a measure of 30º. 2. Each person in the group should draw the triangle with different side lengths, then measure the legs using inches. 3. Compute the ratio leg opposite ﮮ A leg adjacent ﮮ A 4. Compare the ratio with the others in the group. Make a conjecture.

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Trigonometry and the Tangent Ratio Objectives: Use tangent ratios to determine side lengths in triangles Now, we will use Trigonometry (triangle measure). We will investigate 3 of the 6 trigonometric functions: tangent sine cosine Previously, to find measures in a right triangle, we used: Pythagorean Theorem Distance Formula 30-60-90 or 45-45-90 special right triangles theorems

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Trigonometry and the Tangent Ratio Tangent Ratio: In a right triangle, the ratio of the length of the leg opposite ﮮ P to the length of the leg adjacent to ﮮ P In a right triangle, the ratio of the length of the leg opposite ﮮ P to the length of the leg adjacent to ﮮ P. This is called the tangent ratio. Tangent of ﮮ P = opposite leg adjacent leg

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Write a Tangent Ratio Write the tangent ratios for ﮮ T and ﮮ U. tan T = opp = UV = 3 adj TV 4 tan U = opp = TV = 4 adj UV 3

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what is a tangent ratio? We use tangent ratios to determine side lengths and angles in right triangles. In a right triangle, the ratio of the length of the leg opposite to an angle to the length of the leg adjacent to the same angle. This ratio is always constant

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The Tangent Ratio Tangent of

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Writing Tangent Ratios Write the tangent ratios for

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Find the Tangent Ratios Find the tangent ratios for
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Find the Tangent Ratios Find the tangent ratios for
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Solve for the missing side Find the value of w to the nearest tenth: 54° 10 w Start at 54°. We have sides opposite and adjacent of that angle. We can use tangent to solve for the missing side. Set up the tangent ratio: tan 54 = w 10 Cross multiply w = (tan 54)(10) w = 13.8

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Solve for the missing side Find the value of w to the nearest tenth: 57° 2.5 w Start at 57°. We have sides opposite and adjacent of that angle. We will use tangent to solve for the missing side. Set up the tangent ratio: tan 57 = w 2.5 Cross multiply w = (tan 57)(2.5) w = 3.8

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Solve for the missing side Find the value of w to the nearest tenth: 28° 1 w Start at 28°. We have sides opposite and adjacent of that angle. We will use tangent to solve for the missing side. Set up the tangent ratio: tan 28 = 1 w Cross multiply (tan 28)(w) = 1Divide by tan 28 w = 1 tan 28 w = 1.9

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The Tangent Ratio CHAPTER 7 RIGHT TRIANGLE TRIGONOMETRY Solving for Angle Measures

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Using the Inverse of Tangent The Inverse Tangent Button on your calculator looks like this: tan -1 (You must press the “2nd” or “SHIFT” or “INV” Button and then press “tan”) *We use inverse tangent when solving for a missing angle measure

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Using Inverse Tangent Find the m < X to the nearest degree: H B X 5 8 We will use tangent to find the measure of

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Using Inverse Tangent Find the m < Y to the nearest degree: Y TP 25 23 We will use tangent to find the measure of

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Investigate Tangent Ratios 1. Select one angle measure from 20º, 30º, 40º, or 50º. 2. Each person draw a right triangle ( ∆ ABC) where A has the selected.

Investigate Tangent Ratios 1. Select one angle measure from 20º, 30º, 40º, or 50º. 2. Each person draw a right triangle ( ∆ ABC) where A has the selected.

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