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Trigonometry: Solving Lengths & Angles with Sine, Cosine, and Tangent Functions

Learn to find missing lengths and angles in right triangles using trigonometric functions like sine, cosine, and tangent. Discover how to use inverse trigonometry to calculate angles and solve problems efficiently.

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Trigonometry: Solving Lengths & Angles with Sine, Cosine, and Tangent Functions

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  1. Trigonometry (Continued)

  2. C A H S O H T O A

  3. What we know already! O means theta Hyp opp O Adj

  4. Find the missing length Sin O = opposite hypotenuse Sin 30º = Y 15 0.5 = y 15 0.5 x 15 = Y Y = 7.5 15 Y 30°

  5. Finding angles when you know the lengths

  6. What if we know the length and want to find the angle? 14cm Tan O = opposite adjacent Tan O = 14 17 Tan O = 0.8235 Angle O = inv tan 0.8235 Angle O = 39.47º O 17cm

  7. Using the inverse button on your calculator, work out the following angles 1) Sin = 0.6421 6) Sin = 0.8624 7) Tan = 0.5724 2) Cos = 0.7254 = 0.2125 8) Sin = 0.8 3) Tan 9) Cos = 0. 9847 4) Cos = 0.9564 5) Tan = 0.5 10) Tan = 0.7464

  8. Y A 12 AC X 12 20 C B B 25 B A BC C 6.2 X A B 25 X 42º 9 12º 8 C 35º Y D 60 12 33º 35º Y E 20º 28 25 A Please copy the diagrams and find the missing lengths 5 1 30º 30 2 6 40º 70º 3 50 7 23º 30º 4 6.5 8 45º 40º

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