Defining Right Triangles

Let's talk triangles.  Specifically right triangles, triangles with right angles (angles that equal 90°).

The line across from right angle is known as the hypotenuse.  The other two lines are called the legs.  Now enough with this formal stuff that is a thorn in everyone's side.  We will refer to the hypotenuse as "c" and the legs are "a" and "b".  Along with angle(<A) measures the triangle also has lengths for each side.

Angle measurements

<A+<B+<C=180°

To find a unknown angle with two known simply plug in and solve like it was an algebraic equation.

Defining Sides of Triangles

Except in right triangles, any angle may be designated <A, <B, and <C.  The side of the triangle that is directly across from a angle (Ex: <A) is called a, b, or c (Ex: the side directly across from <A would be called a).

Finding Lengths of sides in a right triangle

The Pythagorean Theorem is a useful way of finding the length of legs in a right triangle. The theorem states that a^2 + b^2 = c^2 this means that you take the lengths of the two legs, square them, add them together, and you will get the hyp squared.  To find the length of a leg, with the other leg and the hyp known plug the numbers into the equation and solve like it was an algebraic equation.

Finding Lengths of sides in a any triangle

The Pythagorean Theorem is useful, but it can't be used with every triangle, the following laws can be if you have the neccessary information.

Law of sine

The law of sine states:

sin(A)/a = sin(B)/b = sin(C)/c

This means that the sine of <A divided by the length of side a equals the sine of <B divided by side b which also equals <C divided by side c.

You can use this law if you have the measurements of two angles and the length of a side or the measurement of one angle and the lengths of two sides.

Law of cosine

a^2 = b^2 + c^2 -( 2bc * cos(A))

or

b^2 = a^2 + c^2 - (2ac * cos(B))

or

c^2 = a^2 + b^2 - (2ab * cos(C))

This means that the length of one side squared equals the sum of the suqares of the lengths of the two other sides minus the difference of two times the product of the lengths of the two other sides times the cosine of the angle directly across from the first side.  This may sound cofusin, but this is a very useful tool.

To use this law you need the measurements of two sides and one angle.