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Solving Right Triangles: Techniques and Examples for Angle and Side Calculations

In this guide, we explore the methods for solving right triangles, focusing on finding the measures of all three sides and angles. You'll learn how to use the sine, cosine, and tangent ratios, as well as their inverse functions, to calculate missing parts of a right triangle. Interactive examples demonstrate the application of these techniques, ensuring a solid understanding of the concepts. Whether you're preparing for assessments or looking to enhance your skills, this resource provides clear explanations and examples.

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Solving Right Triangles: Techniques and Examples for Angle and Side Calculations

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  1. Warm-up #3 1. Sin 23o = 2. Cos 78o = 3. Tan 42o = 4. Sin A = 5. Sin B = 6. Cos A = 7. Cos B = 8. Tan A = 9. Tan B = A 13 12 B 5

  2. Solving Right Triangles

  3. 9.6 Solving Rt Δs Essential Question – How do we solve right triangles and their applications?

  4. Solving a right Δ • To solve a rt Δ: find the measure of all its missing parts (should be 3 sides and 3 s). • To find an  measure: If sin A=x, then mA= sin-1x If cos A=x, then mA=cos-1x If tan A=x, then mA=tan-1x

  5. Pull out your calculators For inverse sine (sin-1) press 2nd sin For inverse cosine (cos-1) press 2nd cos For inverse tangent (tan-1) press 2nd tan These are also known as arc sin, arc cos, & arc tan.

  6. Ex: Find the measure of the . sin A=.5 tan B=.1051 mA=sin-1.5 mA=30o mB=tan-1.1051 cos A=.7071 mB=6o mA=cos-1.7071 mA=45o

  7. ExampleSolve the Δ mA=sin-1.96 mA=74o A mB=sin-1.28 25 7 mB=16o __ __ B C 24

  8. Ex:solve the Δ (round to the nearest tenth) C 82+102=b2 __ __ 10 64+100=b2 8 164=b2 B A 12.8=b b mA=51.3o mA= tan-11.25 mB=180-90-51.3=38.7o

  9. Example S 15 r=5.1 r __ 20o __ T R s mS=180-90-20 mS=70o

  10. Examplesolve for x 15.7mi __ x __ 59mi tan x=.2661 x= tan-1.2661 x=14.9o

  11. Assignment

  12. Assessment

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