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Understanding Trigonometry: Basics, Formulas, and Real-Life Applications

This guide introduces the foundational concepts of trigonometry, focusing on right triangles. Learn how to find the lengths of sides and measure angles using sine, cosine, and tangent functions. Understand key definitions such as hypotenuse, opposite side, and adjacent side. Explore essential formulas, including SOH-CAH-TOA, and apply the Pythagorean Theorem to solve problems. Additionally, discover how to calculate unknown angles and real-world applications, such as determining tree heights using shadows. Practice with provided exercises to reinforce your learning.

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Understanding Trigonometry: Basics, Formulas, and Real-Life Applications

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Presentation Transcript

  1. 1.4 Trigonometry

  2. Uses of Trigonometry • Lets you find the length and measure of angles of right triangles • Sine • Cosine • Tangent

  3. Definitions •  = angle • hyp = hypotenuse (longest side) • opp = side opposite (not touching) the angle • adj = side adjacent (touching) the angle

  4. Formulas SOH CAH TOA

  5. A c 5 25° B C a Example 1 • Find side c • c = 11.8 • Find side a • a = 10.7

  6. A c 5 B C 8 Example 2 • Given 2 sides, find the angle • Find A • A = 58.0 • Find B • B = 32.0

  7. Other Rt Triangle Tools • If given 2 side, find 3rd side • Use Pythagorean Theorem • a2 + b2 = c2 • C is the hypotenuse • If given 2 angles, find 3rd angle • Sum of angles = 180 • A + B + C = 180

  8. Example 3 – Word Problem • A tree’s shadow is 3 m long and the sun is at 60° above horizontal. Find the height of the tree. • Height = 5.20 m

  9. Practice Work • You should now be able to complete • 19 #CQ6, 7, P11 – 16 • Total of 8 problems

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