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Key-value pairs

Figure 4 contains the text values associated with each of the Braille keys.

Figure 4 . Text values for Braille keys in file Phy1020b2svg.
m: A 3-4-5 Triangle n: 4o: Vertical axis p: 0q: 0 r: Adjacent sides: 53.13 Degrees t: adju: 3 v: oppw: Opposite side x: hypy: Hypotenuse z: Horizontal axisA: Not drawn to scale

The length of the hypotenuse

Now that you have your right triangle on the graph board, or you have access to tactile graphics created from the svg file, and you know thelengths of the adjacent and opposite sides, do you remember how to calculate the length of the hypotenuse?

The Pythagorean theorem

Hopefully you know that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two othersides. Thus, the length of the hypotenuse is equal to the square root of the sum of the squares of the other two sides.

In this case we can do the arithmetic in our heads to compute the length of the hypotenuse. (I planned it that way.)

The square of the adjacent side is 9. The square of the opposite side is 16. The sum of the squares is 25, and the square root of 25 is5. Thus, the length of the hypotenuse is 5.

A 3-4-5 triangle

You have created a rather unique triangle. You have created a right triangle in which the sides are either equal to, or proportional to the integervalues 3, 4, and 5.

I chose this triangle on purpose for its simplicity. We will use it to investigate some aspects of trigonometry.

The sine and arcsine of an angle

You will often hear people talk about the sine of an angle or the cosine of an angle. Just what is the sine of an angle anyway?

Although the sine of an angle is based on very specific geometric considerations involving circles (see (External Link) ), for our purposes, the sine of an angle is simply a ratio between the lengths of two different sides of a righttriangle.

A ratio of two sides

For our purposes, we will say that the sine of an angle is equal to the ratio of the opposite side and the hypotenuse. Therefore, in the case of the 3-4-5 triangle that youhave on your graph board, the sine of the angle at the origin is equal to 4/5 or 0.8.

If we know the lengths of the hypotenuse and the opposite side, we can compute the sine and use it to determine the valueof the angle. (We will do this later using the arcsine.)

Conversely, if we know the value of the angle but don't know the lengths of the hypotenuse and/or the opposite side, we can obtain the value of the sine of theangle using a scientific calculator (such as the Google calculator) or lookup table.

The sine of an angle -- sample computation

Enter the following into the Google search box:

sin(53.13010235415598 degrees)

The following will appear immediately below the search box:

sin(53.13010235415598 degrees) = 0.8

This matches the value that we computed above as the ratio of the opposite side and the hypotenuse.

The arcsine (inverse sine) of an angle

The arcsine of an angle is the value of the angle having a given sine value. In other words, if you know the value of the sine of an unknown angle, you canuse a scientific calculator or lookup table to find the value of the angle.

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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