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Hypotenuse, opposite, and adjacent

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.
We use special words to describe the sides of right triangles.
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.
The other two sides are called the opposite and adjacent sides. These sides are labeled in relation to an angle.
The opposite side is across from a given angle.
The adjacent side is the non-hypotenuse side that is next to a given angle.
Putting it all together from the perspective of A:
And from B:

Practice

Problem 1
Relative to angle G, which side is the adjacent side?
Choose 1 answer:

Why are these words important?

We're about to learn the trigonometric functions—sine, cosine, and tangent—which are defined using the words hypotenuse, opposite, and adjacent.

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  • blobby green style avatar for user Abdi Aziiz
    who is the largest and the shortest of these three words hypotenuse opposite and adjacent
    (42 votes)
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    • purple pi pink style avatar for user Charlie Auen
      The shortest side is the one opposite the smallest angle. If the angle you already know is the shortest one, then the shortest side is opposite it. However, if the angle you already know is the medium one, then the shortest side is adjacent to it.

      The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle.
      (115 votes)
  • leaf red style avatar for user Jack McClelland
    Can any of the calculations of trigonometry be applied to non-right triangles? Seems like a very niche area if it only covers right triangles.
    (23 votes)
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  • aqualine seed style avatar for user Saad Khan
    why is trigonometry important?
    (17 votes)
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  • winston default style avatar for user Anshuman Parida
    why do we need to learn trigonometry?why are they important?where did the names sine cos tan come from?
    (17 votes)
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    • boggle yellow style avatar for user Gustavo Sáez
      Trigonometry is very useful in any type of physics, engineering, meteorology, navigation, etc... (Wherever geometry is useful, trig is almost certain to also be useful). Trig isn't for everyone, however if little billy wants to calculate how tall a building is without producing the world's longest tape measure, he's gonna need some trig. The name sine (from what i know) comes from the latin word sinus, meaning hole or cavity, basically translation after translation of the word we ended with hole, which turned into sinus, sine for short (I may be wrong, but that is what I remember). The name cosine comes from the fact that sine and cosine are co-functions, (due to the fact that sin(x-90)=cosx. Tangent is not as easy to explain, it has to do with geometry and tangent lines.
      (43 votes)
  • stelly green style avatar for user London Brown
    why do we need to learn trigonometry?
    (6 votes)
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    • stelly orange style avatar for user USER_R_04
      Trigonometry is part of the standard high school curriculum, but it's not an essential subject for nothing. Many career choices involve studying trigonometry, especially STEM fields such as science, engineering, or technology. In the end, it depends on you and your career choice. Because, if anything, trigonometry is very useful for learning physics and astronomy. In some cases, you may have to use trigonometry for videogame design and programming as well. Moreover, at least in college you may have to learn trigonometry as a sort of gatekeeper before you can take core curriculum classes. This may be the case for computer science where students have to learn calculus or even physical therapy. To summarize, you don't have to love trigonometry, but many of the world's most valuable inventions and discoveries couldn't have existed without the math of tirangles, and the same thing applies to the future you want to pursue, whether academic success or honorable achievements.

      (Fun Fact; man wouldn't have landed on the moon if people didn't know/study trigonometry👀)

      It's an interesting math, and though it can be hard, it's the foundation of many amazing works today, but of course you're free to like the subject or dislike it, I'm just here to spread the benefit!🙌

      Hope I helped!🧡
      (38 votes)
  • blobby green style avatar for user logan.vadnais
    Is trigonometry just about triangle?
    (8 votes)
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  • primosaur seedling style avatar for user ok
    Where is it used in real life
    (8 votes)
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  • piceratops seed style avatar for user keyana mcghee
    How do you know which one is the opposite and the adjacent side?
    (7 votes)
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  • boggle blue style avatar for user Allie
    What is cosine and sine?
    (2 votes)
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    • blobby green style avatar for user ohn.y.28
      Cosine equals to the adjacent divided by the hypotenuse, and sine equals to the opposite divided by the hypotenuse. Think of this: soh, cah, and toa. soh means sine = opposite/hypotenuse, cah means cosine = adjacent/hypotenuse, and toa means tangent = opposite/adjacent.
      Hope that helps.
      (18 votes)
  • mr pants teal style avatar for user Arsh  Yadav
    what are the applications of trigonometry in general life?
    (3 votes)
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    • starky ultimate style avatar for user Augustine.Wittkower
      Accurate calculation of distance between points, (if you ever hear the phrase "triangulate their position", that's what's going on!).

      Sine waves and their equations are used for countless things, most anything that behaves like a wave such as sound, light, radio, etc.

      Even things like game design, I was working on a spaceship game where I needed to have the ship turn and move on a 2D plane. Trig is how that problem is solved.
      (8 votes)