Using tangent to find the missing length of a triangle

00:03:39
https://www.youtube.com/watch?v=AtrmL8sxPKg

Summary

TLDRIn this video, the instructor explains how to work with right triangles, focusing on identifying the hypotenuse, adjacent, and opposite sides based on a given angle. The video emphasizes the use of trigonometric functions, particularly the tangent function, to find unknown side lengths. The instructor provides a step-by-step example using a 52° angle and an adjacent side length of 13 to calculate the opposite side length. The importance of ensuring the calculator is in degree mode is also highlighted.

Takeaways

  • 📐 Identify the hypotenuse as the side opposite the right angle.
  • 📝 The adjacent side connects the angle to the right angle.
  • 🔄 The opposite side is directly across from the angle.
  • 📊 Use sine, cosine, and tangent for calculations.
  • 📏 Tangent = opposite / adjacent.
  • 🔍 For a given angle, set up the tangent equation to find unknowns.
  • 🧮 Ensure your calculator is in degree mode before calculations.
  • 🔗 Use known side lengths to solve for unknowns.

Timeline

  • 00:00:00 - 00:03:39

    In this segment, the speaker explains the components of a right triangle, focusing on identifying the hypotenuse, adjacent side, and opposite side relative to a given angle. The hypotenuse is defined as the side opposite the right angle, while the adjacent side connects the angle to the right angle, and the opposite side is directly across from the angle. The speaker emphasizes the use of trigonometric functions (sine, cosine, and tangent) to find unknown side lengths, particularly when the triangle does not conform to special right triangle ratios. Given an angle of 52° and the adjacent side length of 13, the speaker decides to use the tangent function to solve for the opposite side, leading to the equation tangent(52°) = x/13. After rearranging and calculating, the speaker finds the value of the opposite side to be approximately 16.64.

Mind Map

Video Q&A

  • What is the hypotenuse in a right triangle?

    The hypotenuse is the side directly across from the right angle.

  • How do you identify the adjacent side?

    The adjacent side connects the given angle and the right angle.

  • What is the opposite side?

    The opposite side is directly across from the given angle.

  • Which trigonometric functions are used for right triangles?

    The sine, cosine, and tangent functions are used.

  • How do you calculate the tangent of an angle?

    The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

  • What should you check before using a calculator for trigonometric functions?

    Ensure your calculator is in degree mode.

  • How do you solve for an unknown side using tangent?

    Set up the equation using the tangent function and solve for the unknown side.

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Subtitles
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  • 00:00:00
    so on this example ladies and gentlemen
  • 00:00:02
    when you are provided a right triangle
  • 00:00:04
    all right and we're provided an angle
  • 00:00:06
    and a side length the best thing I can
  • 00:00:08
    at least offer to you is at least let's
  • 00:00:09
    label all the sides according to this
  • 00:00:12
    angle regardless of where the angle is
  • 00:00:14
    the hypotenuse is the easiest to
  • 00:00:16
    identify it's directly across from your
  • 00:00:19
    right angle hypotenuse now the next
  • 00:00:22
    definition we talked about is the
  • 00:00:24
    adjacent side compared to the opposite
  • 00:00:26
    side so Camila do you remember how to
  • 00:00:27
    find the adjacent side okay okay so let
  • 00:00:31
    me resay it so if you need to write it
  • 00:00:33
    down Camila you can the adjacent side
  • 00:00:37
    connects your angle and the right angle
  • 00:00:40
    so therefore you can see that the side
  • 00:00:43
    between the angle that is provided and
  • 00:00:45
    the right angle is your adjacent side
  • 00:00:49
    then the other side which is directly
  • 00:00:51
    opposite of your angle is what we call
  • 00:00:54
    the opposite side now we're given a
  • 00:00:57
    right triangle with um an angle and an
  • 00:01:00
    opposite and an adjacent side and we're
  • 00:01:02
    trying to find the value of that side so
  • 00:01:05
    to do that we're going to want to use um
  • 00:01:08
    our right triangle trigonometry right if
  • 00:01:10
    we knew this was a 45 4590 triangle or a
  • 00:01:13
    30 60 90 we could use special right
  • 00:01:14
    triangles but this is not because we
  • 00:01:16
    have an angle of 52° so therefore we
  • 00:01:19
    need to remember our three trigonometric
  • 00:01:21
    functions s cosine and tangent now these
  • 00:01:26
    are all of an angle which I'll use Theta
  • 00:01:29
    as my angle
  • 00:01:30
    and remember the sign function of an
  • 00:01:33
    angle is equal to the opposite over the
  • 00:01:37
    hypotenuse the cosine is equal to the
  • 00:01:39
    ratio of the adjacent side over the
  • 00:01:42
    hypotenuse and the tangent of an angle
  • 00:01:45
    is equal to the ratio of the opposite
  • 00:01:47
    side over the adjacent so now I look at
  • 00:01:50
    each one of those three functions I say
  • 00:01:51
    all right well which side lengths do I
  • 00:01:53
    have I am provided with the value of
  • 00:01:56
    opposite which I'm trying to find and
  • 00:01:58
    I'm provided with the actual angle of
  • 00:01:59
    jent so I don't have anything with
  • 00:02:01
    hypotenuse we're not trying to figure
  • 00:02:02
    out what hypotenuse is and I'm not
  • 00:02:04
    provided the hypotenuse right Camilo so
  • 00:02:07
    therefore any any trigonometric function
  • 00:02:10
    with hypotenuse I'm not going to
  • 00:02:13
    use so I'm only going to use the tangent
  • 00:02:15
    function now do I know the angle of the
  • 00:02:18
    tangent that I'm going to use 52 de do I
  • 00:02:21
    know the opposite side x do I know the
  • 00:02:23
    adjacent side 13 so I can say the
  • 00:02:27
    tangent of my angle 52
  • 00:02:30
    is equal to X over 13 now I just need to
  • 00:02:35
    solve for x so I need to get to 13 off
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    the bottom so what I'll do is I'll
  • 00:02:39
    multiply 13 on both
  • 00:02:43
    sides and therefore x = 13 * the tangent
  • 00:02:49
    of
  • 00:02:50
    52° so I need to go into my
  • 00:02:53
    calculator what you guys somebody stole
  • 00:02:55
    my calculator again but I'll go and grab
  • 00:02:57
    it so now I go ahead and plug into my
  • 00:03:01
    calculator the tangent now make sure
  • 00:03:04
    your calculator is in degree mode if you
  • 00:03:06
    don't know make sure you let me know and
  • 00:03:08
    I'll help you out with that and then I
  • 00:03:10
    just type in Tangent or 13 times the
  • 00:03:12
    tangent of
  • 00:03:17
    52
  • 00:03:19
    and I get 16. 639 so I'll reduce to
  • 00:03:23
    round to the
  • 00:03:25
    100 x
  • 00:03:27
    equal 16
  • 00:03:33
    64 and there we
  • 00:03:36
    go 6
Tags
  • right triangle
  • hypotenuse
  • adjacent side
  • opposite side
  • trigonometric functions
  • tangent
  • sine
  • cosine
  • angle
  • calculator