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Unofficialllyy

  • one year ago

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  1. Unofficialllyy
    • one year ago
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    How do similar right triangles lead to the definitions of the trigonometric ratios?

  2. Unofficialllyy
    • one year ago
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    @jim_thompson5910 Could you try to help?

  3. Unofficialllyy
    • one year ago
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    My notes say this: The term trigonometry comes from a Greek word meaning “triangle measuring.” The sine of an angle within a right triangle is found by dividing the length of the opposite side by the length of the hypotenuse. The cosine of an angle within a right triangle is found by dividing the length of the adjacent side by the length of the hypotenuse. The tangent of an angle within a right triangle is found by dividing the length of the opposite side by the length of the adjacent side. But I am not sure which one is the right answer for the question.

  4. jim_thompson5910
    • one year ago
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    so the question is `How do similar right triangles lead to the definitions of the trigonometric ratios?` and there are no answer choices? it's a fill in the blank kind of question?

  5. Unofficialllyy
    • one year ago
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    This is one of the questions I am going to be asked on my oral test, so I want to make sure I know how to answer it. There are no multiple choice answers.

  6. jim_thompson5910
    • one year ago
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    let's say we had this right triangle |dw:1433986107369:dw|

  7. Unofficialllyy
    • one year ago
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    Alright

  8. jim_thompson5910
    • one year ago
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    cut each length in half to get this similar triangle |dw:1433986215952:dw|

  9. jim_thompson5910
    • one year ago
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    oops typo |dw:1433986258148:dw|

  10. jim_thompson5910
    • one year ago
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    let's say we place the reference angle theta here |dw:1433986304712:dw|

  11. jim_thompson5910
    • one year ago
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    for the large triangle, we know opposite/hypotenuse = 6/10 = 3/5 = 0.6 for the small triangle, we know opposite/hypotenuse = 3/5 = 0.6

  12. jim_thompson5910
    • one year ago
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    the ratio of those two sides forms the sine of the angle theta

  13. jim_thompson5910
    • one year ago
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    so if we want to make a similar triangle, we just need to make sure that the ratio of 0.6 stays the same

  14. jim_thompson5910
    • one year ago
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    |dw:1433986433430:dw|

  15. Unofficialllyy
    • one year ago
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    I just don't understand the question. It should be on the notes page of my lesson but I can't seem to find it.

  16. Unofficialllyy
    • one year ago
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    Do they relate because the sides are always proportional and then the sine, cosine, and tangent is found by dividing the lengths?

  17. jim_thompson5910
    • one year ago
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    you agree that similar right triangles have the same angles right?

  18. Unofficialllyy
    • one year ago
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    Yes

  19. jim_thompson5910
    • one year ago
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    so let's say you didn't have a protractor and you couldn't measure the angles how can you check to see if the two angles are congruent?

  20. Unofficialllyy
    • one year ago
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    Ummm using AAA or the other ones lol

  21. jim_thompson5910
    • one year ago
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    but we know nothing about the angles

  22. jim_thompson5910
    • one year ago
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    let's say you had only a ruler

  23. jim_thompson5910
    • one year ago
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    using the ruler, you can measure the segments but not the angles

  24. Unofficialllyy
    • one year ago
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    Right

  25. jim_thompson5910
    • one year ago
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    you can use the converse of the SSS similarity theorem to say if the sides are in proportion, then the triangles are similar which will lead you to concluding the angles are congruent

  26. jim_thompson5910
    • one year ago
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    with right triangles, you only need to worry about 2 sides (not all 3) and the trig functions are simply ratios of the sides

  27. Unofficialllyy
    • one year ago
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    So how do similar right triangles and the trig ratios relate? I don't get it

  28. jim_thompson5910
    • one year ago
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    For similar right triangles, the sine ratio will stay the same. The cosine ratio will stay the same. The tangent ratio will stay the same

  29. jim_thompson5910
    • one year ago
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    Again the trig ratio is used to connect the angle with two sides the angle will stay the same since we're dealing with similar triangles (with congruent angles)

  30. Unofficialllyy
    • one year ago
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    Oh so the trigonometric ratios will always be the same with similar right triangles

  31. jim_thompson5910
    • one year ago
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    |dw:1433987739690:dw|

  32. jim_thompson5910
    • one year ago
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    as long as theta stays where it is, for any other similar triangle you can think of, the sine ratio will stay put at 0.6

  33. jim_thompson5910
    • one year ago
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    the sides may change, but their relationship or ratio will stay the same

  34. jim_thompson5910
    • one year ago
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    for example, the opposite side may turn into 600, but the hypotenuse will also change to 1000 600/1000 = 0.6 the sine ratio stays the same

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