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Trigonometry: Calculate Angles & Sides of Right Triangles II

Use trigonometry to find unknown angles in right triangles with given side lengths. Learn to apply the tangent function for accurate calculations.

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Trigonometry: Calculate Angles & Sides of Right Triangles II

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  1. Trigonometry Basic Calculations of Angles and Sides of Right Triangles

  2. Part II Use trigonometry to determine the size of an angle.

  3. Determine an unknown angleExample 1 • To start, we will determine the size of an unknown angle when two sides of the right triangle are known. 5.5” A 12”

  4. Determine an unknown angleExample 1 • Let the unknown angle A be the reference angle. 5.5” A 12”

  5. Determine an unknown angleExample 1 • Now label the sides of the right triangle... opposite hypotenuse 5.5” A adjacent 12”

  6. Determine an unknown angleExample 1 • Note that we only know the lengths of the opposite and adjacent sides. opposite hypotenuse 5.5” A adjacent 12”

  7. Determine an unknown angleExample 1 • So we need to pick a trig function that has the opposite and adjacent sides in it... opposite 5.5” A adjacent 12”

  8. Determine an unknown angleExample 1 • Which trig function should you pick? You need to pick the tangent function since it is the only one that has both opposite and adjacent sides in it. 5.5” opposite A 12” adjacent

  9. Determine an unknown angleExample 1 • Now plug-in the numbers you have into the tangent function... opposite A = 24.6° Now use your calculator to solve. Type-in .458333, press the 2nd function key, then press the tan key 5.5” A adjacent 12”

  10. Determine an unknown angleExample 1 • How could you determine the size of the remaining angle? …this one must be 65.4° degrees. (Since 180° - 90° - 24.6° = 65.4°) 65.4° ..and this one was computed to be 24.6°… 5.5” This angle is 90°… 24.6° 12”

  11. 35 mm A 31.5 mm Determine an unknown angleExample 2 • Let’s try another one… • Determine the size of angle A.

  12. Determine an unknown angleExample 2 • To determine the other angle: • 180° - 90° - 25.8° = 64.2° 64.2° 35 mm 25.8° 31.5 mm

  13. 125 mm 132 mm A Determine an unknown angleExample 3 • Let’s try one more. • Determine the size of angle A.

  14. Determine an unknown angleExample 3 • The angle is computed to be 18.7°. 125 mm 18.7° 132 mm 71.3°

  15. Homeworkpg. 485 #3pg. 486 #7, 10,12,14,19,20

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