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Investigate Tangent Ratios

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 measure. 3. Each person make the triangle different sizes. Then measure the legs using inches.

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Investigate Tangent Ratios

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  1. 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 measure. 3. Each person make the triangle different sizes. Then measure the legs using inches. 4. Compute the ratio leg opposite A leg adjacent A 5. Compare the ratio with others that selected the same angle measure. Make a conjecture.

  2. Section 9-1 Trigonometry and the Tangent Ratio SPI 32F: determine the trigonometric ratio for a right triangle needed to solve a real-world problem given a diagram • Objectives: • Use tangent ratios to determine side lengths in triangles • Previously, to find measures in a right triangle, we used: • Pythagorean Theorem • Distance Formula • 30-60-90 or 45-45-90 triangle theorems • Now, we will use Trigonometry (triangle measure). • We will investigate 3 of the 6 trigonometric functions: • tangent • sine • cosine

  3. Trigonometry and the Tangent Ratio • Tangent Ratio: • In a right triangle, the ratio of the length of the leg opposite P to the length of the leg adjacent to P is constant, no matter what lengths are chosen for the sides. This is called the tangent ratio. Tangent of P = opposite leg adjacent leg

  4. opposite adjacent Tangent A = Write a Tangent Ratio It is just a formula!!!! Do Now Write the tangent ratios for T and U. tan T = opp = UV = 3 adj TV 4 tan U = opp = TV = 4 adj UV 3

  5. Apply Tangent to Real-World Suppose you are snow skiing in Colorado and get lost. You can see a cliff in the distance which is where the ski lodge is located. About how far away is the cliff? 86° 50’ Draw a diagram Step 1: Point your compass towards the cliff. Take a reading. Step 2: Turn 90 degrees and walk 50 feet in a straight path. Step 3: Point your compass towards the cliff. Take a reading. Solution Suppose in step 3, you find the measure of angle from where you stand to the cliff is 86. Now find the distance to the cliff using the tangent ratio. tan 86 = x 50 x = 50 tan 86 = 715 The cliff is about 715 feet away.

  6. Inverse of a Tangent If you know the tangent ratio of an angle, finding the unknown angle is called the inverse tangent and is written as tan-1. Find the mY. 1. First find the tan ratio. tan Y = 100 = 2.44 41 2. Take the tan inverse of the ratio. m Y = tan-1 (2.44) = 68

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