this presentation will briefly describe about applications of trigomery. useful for class x cbse students
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4.8 Applications and Models using Trigonometry
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Given one side and an acute angle of a right triangle Find the remaining parts of the triangle. = 45.90 mZB = = 900 mZC b = 12.8
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Given one side and an acute angle of a right triangle Find the remaining parts of the triangle. 12.8 cos45.90 = 49.50 12.8 C 12.8 cos45.90 18.4
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Given one side and an acute angle of a right triangle Find the remaining parts of the triangle. a Tan45.90 = 12.8 12.8 Tan45.90 = a a 13.2 49.50 12.8
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Given one side and an acute angle of a right triangle Find the remaining parts of the triangle. For Angle B 900 — 45.90 = 44, 10 13.2 49.50 12.8
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Find of an object in the distance Finding the height of a tree on a mountain. 58 2 IOOOft
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Find of an object in the distance Finding the height of a tree on a mountain. Tan220 = 1000 1000 • Tan220 = M 404.03 M 58 2 IOOOft
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Find of an object in the distance Finding the height of a tree on a mountain. Tan220 = 1000 1000 • Tan220 = M 404.03 M 58 2 IOOOft Tan580 = 1000 1000 • Tan580 = 404.03 + T
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Trigonometry and Bearings Bearing is an acute angle based off the N 38Q W North - South line. 38
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A nautical problem A yacht is going 14 knots East for 3 hours, then turns N 42Q E for an hour. How far from port is the yacht. : 420
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A nautical problem Need to find a hypotenuse of a larger triangle. To find the distance. : 420
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A nautical problem The extension helps us find the hypotenuse. We have a few angles and the distance to add. : 420
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A nautical problem The extension helps us find the hypotenuse. We have a few angles and the distance to add. 14(3) = 42 14 a : 420 480 b
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A nautical problem The extension helps us find the hypotenuse. We have a few angles and the distance to add. 14(3) = 42 4 14 a : 420 480 b a Sin 480 = 14 14. Sin480=a 10.4
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A nautical problem The extension helps us find the hypotenuse. We have a few angles and the distance to add. 14(3) = 42 14 : 420 480 b b COS480 = 14 14 ' cos480 = b 9.36 -b
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A nautical problem The extension helps us find the hypotenuse. We have a few angles and the distance to add. 14(3) = 42 14 : 420 480 b b COS480 = 14 14 ' cos480 = b 9.36 -b
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A nautical problem The extension helps us find the hypotenuse. We have a few angles and thedistance to add. 51.362 -k 42 42 -k 9.36 52.4 14 : 420 480 9.36 = 51.36
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Harmonic Motion (Doing the Wave) Way of writing the Sine function or Cosine function with time. d = a Sin wt or d = a Cos wt d is the distance from the origin or Equilibrium a is for amplitude; w is like b in the normal function (changes period) Period = Frequency = 27T
Discussion
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