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Section 14.3

Right Triangles and Trig Ratios. Section 14.3. Basic Ratios. We can use basic trig ratios to solve for missing parts of right triangles Ratios do not depend on the size of the triangle, but on the acute angles The six trig ratios are: sin θ = opposite/ hyp csc θ = hyp /opposite

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Section 14.3

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  1. Right Triangles and Trig Ratios Section 14.3

  2. Basic Ratios • We can use basic trig ratios to solve for missing parts of right triangles • Ratios do not depend on the size of the triangle, but on the acute angles • The six trig ratios are: sin θ = opposite/hypcsc θ = hyp/opposite cos θ = adjacent/hyp sec θ = hyp/adjacent tan θ = opposite/adjacent cot θ = adjacent/opposite

  3. Find the trig values I Find the indicated values: 1) sin G 2) sin I 3) cot G 9/41 40/41 40/9 4) cscG 5) cosI 6) sec H 41/9 9/41 Undef 41 G H 40

  4. Building a Right Triangle • Descriptions always will tell you where the right angle is • Use the Pythagorean Theorem to find missing sides • Use arc trig functions to find missing angles In ΔABC, C is the right angle. Find the remaining sides and angles. Round to the nearest tenth. 7) a = 5, b = 6 c= 7.8, A = 39.8˚, B = 50.2˚ 8) a = 17, c = 22 b = 14.0, A = 50.6˚, B = 39.4˚

  5. Using Triangles • The bases on a baseball diamond form a square 90 ft on a side. The pitchers plate is 60 ft 6 in from the back corner of Home Plate. • How far is the pitcher’s plate from Second Base? 66 ft 9.6 in • How far is the pitcher’s plate form First Base? 63 ft 8.4 in • If a line drive is 10 ft high when it passes the Third Baseman 100 ft from Home Plate, at what angle did it leave the bat after making contact? (Assume the ball was hit at a height of 4 ft.) θ ≈ 5.7˚

  6. Homework For tomorrow: Page 782 #2 – 24 even

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