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## High school geometry

### Unit 5: Lesson 4

Ratios in right triangles# 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 angle, A:

And from angle, B:

## Practice

## 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.

## Want to join the conversation?

- 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.(17 votes)
- They sure can! You learn about the unit circle in Precalculus! The unit circle is far more complicated than right triangle trig though, you might want to wait a while before learning it. :)

Happy holidays!!(35 votes)

- why is trigonometry important?(7 votes)
- Trigonometry is about understanding triangles, and every other polygon can be disassembled into triangles. So trigonometry becomes an important aspect of all of plane geometry.(23 votes)

- Is trigonometry just about triangle?(7 votes)
- Yes the roots come from tri (three) gono (angle) metry (measure)

see http://mathforum.org/library/drmath/view/52595.html(14 votes)

- How do you know which one is the opposite and the adjacent side?(4 votes)
- The problem will say, "relative to angle ___." Connect that angle to the right angle in the triangle, and that's the adjacent side. Then you know the hypotenuse(opposite of the right angle) and the adjacent side, so the only other side must be the opposite side.(7 votes)

- Where is it used in real life(6 votes)
- The GPS satellite system to tell where you are, surveying, building, anime, etc.(13 votes)

- who is the largest and the shortest of these three words hypotenuse opposite and adjacent(2 votes)
- 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.(4 votes)

- Why is trigonometry associated with right angled triangles? Why not equilateral, obtuse and acute?(6 votes)
- trigonometry does not only involve right angle triangles it involves all types of triangles,

use of rules such as the sine rule and the cosine rules are applicable

sine rule; (a/sinA)=(b/sinB)=(c/sinC)

cosine rule; a^2= b^2+c^2 - 2bccosA

Well there is a tangent rule...

(a-b)/(a+b)=(tan(a-b/2))/(tan(a+b/2))(2 votes)

- what are the applications of trigonometry in general life?(2 votes)
- 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.(7 votes)

- can you do this stuff with circles.(3 votes)
- Contrary to what another answerer said, circles
*can*be used in conjunction with trigonometry. For example:

Divide a circle into four quadrants.

You now have four right angles.

Do some other stuff and you have a triangle.

Example program made by me: https://www.khanacademy.org/computer-programming/trigonometry-demonstration/6236474914308096

It's animated too.(2 votes)

- why is it called trigonometry..is it because it has 3 sides?(2 votes)
- "trigon" is the greek word for triangle. "me" is a form of the greek word to "measure". So, trigonometry is about the measurement of triangles.(2 votes)