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Mastering Right Triangle Trigonometry: Ratios, Angles, and Side Calculations

This guide explores right triangle trigonometry, focusing on identifying trigonometric ratios—sine, cosine, and tangent—using the mnemonic SOHCAHTOA. Learn to calculate the lengths of missing sides and the measures of angles in right triangles. Step-by-step examples demonstrate labeling triangles, selecting the appropriate ratio, setting up equations, and utilizing inverse functions. Plus, practice problems are included to solidify your understanding. Perfect for students seeking a comprehensive understanding of right triangle trigonometry in various applications.

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Mastering Right Triangle Trigonometry: Ratios, Angles, and Side Calculations

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. Chapter 10 – Section A Right Triangle Trigonometry Objectives To identify the trig ratios of a right triangle. To find the missing side or angle of a right triangle.

  3. opposite hypotenuse opp hyp adjacent adj

  4. 1) In the diagram find: the hypotenuse side opposite angle A side adjacent to angle A side opposite angle C side adjacent to angle C

  5. Chapter 10 – Section B: Trigonometric Ratios The Trigonometric Functions SINE COSINE TANGENT

  6. SOHCAHTOA hyp opp adj

  7. 2) For the triangle shown, find:  sin cos tan 

  8. Finding Sides: Label the triangle with hyp, opp, adj, Choose the correct ratio from SOHCAHTOA Set up the equation Solve.

  9. 65° 10.2 cm x Find, to 3 significant figures, the unknown length in: 3) 4) 8.3 cm x 55°

  10. x 23° 6 34 37° y Find, to 3 significant figures, the unknown length in: 5) 6)

  11. Finding Angles: • Label the triangle with hyp, opp, adj, • Choose the correct ratio from SOHCAHTOA • Set up the equation • Solve by using the inverse. • Calculator must be in DEGREE mode!

  12. Find, to 1 decimal place, the measure of the angle marked  in: 7) 8) 4 2.67 5.92 θ θ 7

  13. 20 θ 21 Find, to 1 decimal place, the measure of the angle marked  in: 10) 9)  2 5

  14. Find to 4 sig. figs the unknowns in the following diagrams: 11) 12)

  15. Homework • 10A, pg 318 • #1 • 10B.1, pg 319 • #1ace • 10B.2, pg 321 • #2acegi, 3ac • 10B.3, pg 323 • #1 acegi, 2a

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