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Understanding Right Triangle Trigonometry: Angles, Degree Measurements, and Theorems

This chapter covers the fundamentals of right triangle trigonometry, including angle measurements in degrees, minutes, and seconds. It explains the conversion from degrees to decimal format and vice versa. The Pythagorean Theorem is thoroughly discussed, with examples showcasing its applications in solving for unknown sides of triangles. Additionally, concepts of latitude and longitude are introduced, helping to understand Earth's grid system. The chapter also covers similar triangles and their properties, essential for various applications in geometry.

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Understanding Right Triangle Trigonometry: Angles, Degree Measurements, and Theorems

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  1. Chapter 1 c a b Right Triangle Trigonometry

  2. 1.1 Angles and Degree Measure A. Degree Measure 1 degree or 1° 1 of the circle 360

  3. 1° 1 minute 1’ 1 of a degree 60

  4. 1’ 1 second 1” 1 of a minute 60

  5. B. Degrees, Minutes, Seconds → decimal 25 45 → 30.4292° 30° 25’ 45”→ 30 + + 60 3600 67° 38’ 12”→ → 67.6367° 123° 50”→ → 123.0139° 33’ 44”→ → .5622°

  6. C. Pythagorian Theorem 13 in. c 5 in. a b 2 2 2 a + b = c 2 2 2 5 + b = 13 b = 12 or -12 2 25 + b = 169 2 b = 144

  7. C. Pythagorian Theorem 15 in. c x in. a b (x + 3) in. 2 2 2 a + b = c

  8. C. Pythagorian Theorem (x + 14) ft c (x – 2) ft a b (2x) ft. 2 2 2 a + b = c

  9. Parallels of Latitude Equator Slicing the Earth into pieces

  10. Measuring Parallels Give the slices values

  11. Lines of Longitude Antimeridian A Meridian A Establish a way of slicing the Earth from pole to pole

  12. Prime Meridian Establishes an orthogonal way of slicing the earth

  13. Longitude North America Values of pole-to-pole slices

  14. Earth Grid Comparing the parallels and the lines

  15. Latitudes and Longitudes Combining the parallels and the lines

  16. 1.2 Similar Triangles ABC ~ ADE A A D E ► ► B C ► ►

  17. 1.2 Similar Triangles A ABC ~ ADE d e D E f A b c B C a

  18. 1.2 Similar Triangles a b c = = A f d e d e D E a f = f d b A b c B C a

  19. 1.2 Similar Triangles A 10 in. 12 in D E f = 15 in A b = 16 in. 2 20 in. 3 B C 25 in.

  20. K PQR ~ JKL 28 cm. 35 cm. J P 24.5 cm. 40 cm. 35 cm. L R Q 50 cm.

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