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Trigonometry

Trigonometry. Basic Calculations of Angles and Sides of Right Triangles. Introduction. You can use the three trig functions ( sin , cos , and tan ) to solve problems involving right triangles. Using a Calculator. 74. or. 74. 74. or. 74. 74. or. 74. cos. sin. sin. tan. tan.

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Trigonometry

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

  2. Introduction • You can use the three trig functions (sin, cos, andtan) to solve problems involving right triangles.

  3. Using a Calculator 74 or 74 74 or 74 74 or 74 cos sin sin tan tan cos 0.961261695 0.275637355 3.487414444 Enter Enter Enter You can use a calculator to approximate the sine, the cosine, and the tangent of 74º. Make sure your calculator is in degree mode. The table shows some sample keystroke sequences accepted by most calculators. 0.9613 0.2756 3.4874

  4. Find a missing side length Use trigonometry to determine the length of a side of a right triangle.

  5. Determining the length of a sideExample 5 • In this problem, we will determine the length of side x. 9” x 26°

  6. Determining the length of a sideExample 5 • As always, first label the sides of the triangle... hypotenuse 9” opposite x 26° adjacent

  7. Determining the length of a sideExample 5 • Since you know the length of the hypotenuse and want to know the length of the opposite side, you should pick a trig function that contains both of them... hypotenuse 9” opposite x 26°

  8. Determining the length of a sideExample 5 • Which trig function should you pick? You need to pick the sine function since it is the only one that has both the opposite side and hypotenuse in it. hypotenuse 9” x opposite 26°

  9. Use basic algebra to solve this equation. Multiply both sides of the equation by 9 to clear the fraction. Determining the length of a sideExample 5 • Now set-up the trig function: hypotenuse 9” opposite x 26°

  10. Determining the length of a sideExample 5 • Now you know the opposite side has a length of 3.95”. hypotenuse 9” opposite 3.95” 26°

  11. x 75 mm 47° Determining the length of a sideExample 6 • Let’s try another one. • Determine the length of side x.

  12. x 75 mm 47° Determining the length of a sideExample 6 • Since the known angle (47°) will serve as your reference angle, you can label the sides of the triangle... opposite adjacent hypotenuse

  13. x 75 mm 47° Determining the length of a sideExample 6 • You know the length of the hypotenuse and want to know the length of the adjacent side, so pick a trig function which contains both of them... adjacent hypotenuse

  14. x 75 mm 47° Determining the length of a sideExample 6 • Which trig function should you pick? You need to pick the cosine function since it is the only one that has both the adjacent side and hypotenuse in it. adjacent hypotenuse

  15. Use basic algebra to solve this equation. Multiply both sides of the equation by 75 to clear the fraction. To finish, evaluate cos 47° (which is 0.682) and multiply by 75. x 75 mm 47° Determining the length of a sideExample 6 • Set-up your trig function... adjacent hypotenuse

  16. Determining the length of a sideExample 6 • Now you know the length of the adjacent side is 51.1 mm. 51.1 mm 75 mm adjacent hypotenuse 47°

  17. Determining the length of a sideExample 7 • Let’s try a little bit more challenging problem. • Determine the length of side x. x 12 ft 35°

  18. Determining the length of a sideExample 7 • Label the sides of the right triangle... hypotenuse x opposite 12 ft 35° adjacent

  19. Determining the length of a sideExample 7 • Which trig function will you pick? You know the length of the side opposite and want to know the length of the hypotenuse. hypotenuse x opposite 12 ft 35° adjacent

  20. Determining the length of a sideExample 7 • Which trig function should you pick? You need to pick the sine function since it is the only one that has both the opposite side and hypotenuse in it. hypotenuse opposite x 12 ft 35°

  21. Use algebra to solve this equation. Multiply both sides of the equation by x to clear the fraction. Next, divide both sides by sin35° to isolate the unknown x. Determining the length of a sideExample 7 • Now set-up your trig function. hypotenuse x opposite 12 ft 35°

  22. 35 cm 50° x Determining the length of a sideExample 8 • The reason the last problem was a little bit more difficult was the fact that you had an unknown in the denominator of the fraction. • Keep clicking to see a similar trig function solved.

  23. 65° 45.5 mm y x Determining the length of a sideExample 9 • Your turn. • Determine the lengths of sides xandy.

  24. 65° 45.5 mm y x Determining the length of a sideExample 9 • Since you want to know the length of side y (adjacent) and you know the length of the hypotenuse, which trig function should you select? hypotenuse adjacent opposite

  25. 65° 45.5 mm 19.2 mm 25° 41.3 mm Determining the length of a sideExample 9 • Both sides have been determined, one by trig, the other using the Pythagorean Theorem. • Also the size of the other acute interior angle is indicated...

  26. 60° x 7.5” Summary • After viewing this lesson you should be able to: • Compute the length of any side of a right triangle as long as you know the length of one side and an acute interior angle.

  27. write answer only as fraction } Homework pg. 469 #3,13pg. 477 # 3,6,7pg. 469 #6,8pg. 470 #18 (no check),28 pg. 477 # 11,14

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