The laws and formulae used
Right Triangles
Pythagoreas's Theorum (aka The Pythagorean Theorum)
This is the basis of all right-angle trigonometry. It is used only for right triangles; those triangles which have an angle of exactly 90 degrees, or pi/2 radians. It is as follows:A2 + B2 = C2
Where A and B are the two shortest sides (legs) and C is the longest
side (hypoteneuse). This theory can be expanded to account for 3
dimensions:
A2 + B2 + C2 = D2
4 dimensions:
A2 + B2 + C2 + D2
= E2
and so on. As long as the longest side (hypoteneuse) is on the right of
the equation.
In order to solve this equation, you must isolate the unknown variable. Suppose we know the legs (variablesA & B), and want to find the hypoteneuse (C). We would simply take the square root of both sides. he resulting equation would be:
sqrt( A2 + B2 ) = sqrt( C2
)
The square root of C
2
is C. We have isolated the hypoteneuse, and the resulting equation is:
sqrt( A2 + B2 ) = C
Let's try another one. Say we want to find the variable B. We would have
to isolate it as such :
A2 + B2 - A2
= C2 - A2sqrt( B2 ) = sqrt( C2 - A2
)
B = sqrt( C2 - A2 )
Basic Trigonetric Functions
There are 6 basic functions in trig: sine (sin), cosine (cos),
tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). An
easy way to remember these functions are SOHCAHTOA (so kah toe uh) --
SinOppHypCosAdjHypTanOppAdj. The Ø is the symbol for an angle, opp
means the side opposite the angle, adj means the side adjacent the
angle, and hyp means the hypoteneuse. The formulas are: 
Sin
Ø = Opp / Hyp
Cos Ø = Adj / Hyp
Tan Ø = Opp / Hyp
sec Ø = hyp / opp
csc Ø = hyp / adj
cot Ø = hyp / adj
The secant, cosecant, and cotangent is the recipricol of the sine,
cosine, and tangent, respectively.
Laet's say you wanted to know the angle based on the side opposite it,
and the hypoteneuse. You would use the equation sin Ø
= opp / hypThe first step is to isolate the variable.
Ø = sin-1 (opp / hyp)Then solve the
equation.
A note on the inverse sine, or arcsine function. The inverse sine (in
notation, is sin-1or asin) is NOT the same as sin(opp
/ hyp)-1. sin(opp / hyp)-1 is the same as sin(hyp
/ opp).
Other Triangles
- We can classify problems of solving triangles into the
following four cases based on the given parts.
Case A.K.A. Definition Solved with Case 1 SAA or ASA One side and two angles Law of Sines Case 2 SSA Two sides and the angle opposite one of them Ambiguous Case Case 3 SAS Two sides and the included angle Law of Cosines Case 4 (SSS) Three sides Law of Cosines Law of sines(Case 1 triangles)
The Law of Sines is as follows:
sinA/a = sinB/b = sinC/cWhere A, B, and C are the angles, and a, b. and c are the sides opposite A, B, and C, respectively. (ex: a is the side opposite angle A, etc.)
