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Textbook: Chapter 13

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** Make sure that your calculator is set to the proper mode**

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Parts Of A Right Triangle Leg Hypotenuse Leg Right Angle Acute Angles

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The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. “No man is free who cannot control himself.” ― Pythagoras of Samos

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The sides of special right triangles (45-45-90 and 30-60- 90) have special relationships (ratios) Given one side of a certain right triangle, we can use these relationships (ratios) to unlock the other two sides. Why is this important if we already know the Pythagorean Theorem? We must know 2 sides of a right triangle to use the Pythagorean Theorem.

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Opposite Hypotenuse Adjacent Opposite Adjacent Hypotenuse

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Trigonometric Ratio – a ratio of the lengths of two sides of a triangle. Sine (sin), Cosine (cos) and Tangent (tan) are the 3 basic trigonometric ratios TanSin Cos

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5 65

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O H O A

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A H

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Solving a right triangle means to find the measure of three angles of the triangle and three sides of the triangle. In other words all six parts. You can solve a right triangle if you know: (1) Two side lengths OR (2) One side length and one angle measure

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A= a= B= b= C= c=

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A= a= B= b= C= c=

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Angle of Elevation vs. Angle of Depression Angle of Elevation = Angle of Depression

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Angle of Elevation vs. Angle of Depression You are standing on top of a building that is 50 ft. tall and you see your buddy on the street. He is standing 30 ft. from the base of the building. Find the angle of depression between you and your buddy.

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60 ft

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175 ft 200 ft Angle of Depression

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