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Right Triangles & Trigonometry

Right Triangles & Trigonometry. OBJECTIVES: Using Geometric mean Pythagorean Theorem 45 °- 45 °- 90 ° and 30°-60°-90° rt. Δ’s trig in solving Δ’s. A. C. Geometric Means. D. B. Finding the geometric mean between a & b:

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Right Triangles & Trigonometry

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  1. Right Triangles & Trigonometry OBJECTIVES: Using Geometric mean Pythagorean Theorem 45°- 45°- 90° and 30°-60°-90° rt. Δ’s trig in solving Δ’s

  2. A C Geometric Means D B Finding the geometric mean between a & b: • The altitude from the 90°angle of a rt. Δ forms 2 similar rt. Δ’s • This altitude is the geometric mean between the 2 hypotenuses and forms the proportion:

  3. The Pythagorean Theorem The sum of the square of legs = hypotenuse 2 • A Pythagorean Triple is a group of 3 numbers that ‘fits’ the Pythagorean Theorem such as 3-4-5, 5-12-13, 7-24-25, 8-15-17,… a2 + b2 = c2 c a b

  4. Special Right Triangles In a 45°- 45°- 90° Δ, the hypotenuse = In a 30°-60°-90° Δ, the hyp = 2 • shorter leg the longer leg = shorter leg ( the shorter leg is opposite the 30 ° angle & the longer leg is opposite the 60° angle) x x 30° 2x x

  5. B Trig Ratios in Right Triangles hypotenuse opp / A c a A b C adjacent to / A Trig Ratio Definition Sine of / A = sin A = Cosine / A = cos A = Tangent / A = tan A = Trig ratios use the acute angles of a rt. Δ. Start with / & find the side opp & the side adj.

  6. Using trig: Angles of elevation & depression Angle of elevation • Angles of elevation & depression are measured from a line // to horizon ( looking up or down) • Use trig ratios to solve for distances, height, etc ~~~~~~~~~~~~~~~~~~~~~~~

  7. Law of Sines B c a To solve any triangle (not just a rt. Δ), use the Law of Sines to help find the 3 angles & the 3 sides Given: B = 39° & C = 88 °, b = 10 A b C Use the first two fractions & cross mult for a; then use the 2nd & 3rd fractions for c

  8. Use Law of Cosines with any Δ C b a A c B • Use law of Cosines once when the info doesn’t fit for the law of Sines, then use law of Sines • Use the formula for the angle you’re given. Be careful!

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