Marked June 7th

Triangles

Definition: Triangles are three sided polygons, with angles adding up to 180 degrees.

triangle_1.gif


Types of Triangles There are many different types of triangles including: equilateral, isosceles, scalene, right, obtuse, and acute.



Equilateral Triangle - An equilateral triangle is a triangle with three equal side lengths and three equal angles of 60 degrees.

equalateral_2.jpg
Isosceles Triangle
An isosceles triangle has only two equal side lengths and two equal angles.


isosolese.jpg

Scalene Triangle
A scalene triangle has no equal sides, and no equal angles.


triangle-scalene.gif

Right Angle Triangle

A right angle triangle has one 90° internal angle.The side opposite to the right angle is the hypotenuse which it is the longest side in the right triangle. The other two sides are the legs of the triangle.
external image hypotenuse.gif
Obtuse Angle Triangle
A obtuse angle triangle has one internal angle that is greater than 90°. It is also an Oblique triangle ( no internal angle equal to 90° )
460px-Triangle-obtuse.svg.png
Acute Angle Triangle
An acute angle triangle has no angles greater then 90°. It is also and oblique triangle.

460px-Triangle-acute.svg.png

Perimeter & Area


To calculate perimeter of a triangle we use P=s+s+s.
Remember to always use units, and never put a ² or a ³ because those are for area and volume
perimeter_triangle.jpg
P=s+s+s
=7+4+7
=18cm

To calculate the area of a triangle we use A=bh/2
Remember to include units, the ² behind your units, ie: cm², m², km², and to divide by 2 at the end!area_triangle.jpg

A=bh/2
=(4)(6)/2
=24/2
=12cm²

Pythagorean Theorem


In math, we use Pythagorean theorem to find the missing side of a right angle triangle. For example:
pythagorim_therom.jpg
Ok, so if we wanna find the missing side length, or "c", we use c²=a²+b²
( A and B can be any measurement that is there on the line, it doesn't matter the order, but C will always be the hypotenuse)
So...
c²=a²+b²
c²=4²+5²
c²=16+25
c²=41
/c²=/41
c=6.4 (rounded) -or- /41

There is also a couple other ways in solving a triangles missing sides rather than using the Pythagorean theorem.

  • Sines: sin A = a/c, sin B = b/c.
  • Cosines: cos A = b/c, cos B = a/c.
  • Tangents: tan A = a/b, tan B = b/a.

Meaning of the word...
Sines: Ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle
Cosines: Ratio of the adjacent side to the hypotenuse of a right-angled triangle
Tangents: Ratio of the opposite to the adjacent side of a right-angled triangle
Adjacent: Things are next to each other. (Beside)


Real World Application


There is many other uses for triangles besides just math, they are used in lots of modern day structures like housing, bridges, electric pylons, and artwork can also be used in flags and signs.
bridge2.jpgbridge1.jpgtriangle_2.jpgtower.jpg
roof-truss-2.jpg
roof-truss-2.jpg
triangle4.jpgexternal image 800px-Flag_of_the_Czech_Republic_%28bordered%29.svg.png

external image star_of_david_lg.jpg
Citations:
Triangles (2005). Retrieved December 10, 2008, from http://www.mathsisfun.com/triangle.html

Joyce, D. E. (1999). Right Angles. Retrieved December 18, 2008.


Pictures:

scalene triangle - http://www.mathsisfun.com/triangle.html
right angle triangle - http://www.mathopenref.com/images/triangle/hypotenuse.gif
obtuse angle triangle - http://mathworld.wolfram.com/ObtuseTriangle.html
acute angle triangle - http://commons.wikimedia.org/wiki/File:Triangle-acute.svg roof truss picture - http://www.renovation-headquarters.com/images8/roof-truss-2.jpg
other triangle-http://www.emis.de/journals/EJC/Surveys/ds5/gifs/5-VD-triangles.gif

Real World Application Pictures:

http://www.rogersconnection.com/triangles/images/bridge2.jpg
http://www.rogersconnection.com/triangles/images/bridge1.jpg
http://www.pinnacleluxurytours.com/images/france_itinerary1/04-Eiffel%20Tower.jpg
http://image34.webshots.com/34/3/72/87/2662372870081606937cfqRrb_fs.jpg
http://www.travelblog.org/World/flags/bahamian-large-flag-bf.gif

http://www.istockphoto.com/file_thumbview_approve/2960168/2/istockphoto_2960168-triangle-sign-clear.jpg
Created By:
Brandon E
Jared W
Will H