


where
A represents the angle of reference. 

The formulas can be remembered by:
oh heck,
another hour
of algebra! 

The formulas can be remembered by:
oscar had
a heap
of apples 

There are many such memory
tricks. 

Basic
Trigonometry Rules:

These
formulas ONLY work in a right
triangle.

The
hypotenuse is always across from the right angle.

Questions
usually ask for an answer to the
nearest units.

You
will need a scientific or graphing calculator.


How to set up and
solve a trigonometry problem when solving for a side of the triangle: 
Example 1:
In
right triangle ABC, hypotenuse AB=15 and angle
A=35º.
Find leg length, BC, to the nearest tenth.

Set
Up the Drawing:
 Draw a picture depicting the situation.
 Be sure to place the degrees
INSIDE the triangle.
 Place a stick figure at the
angle as a point of reference.
 Thinking of yourself as the
stick figure, label the opposite side (the side across
from you), the hypotenuse (across from the right angle), and the
adjacent side (the leftover side).
 Notice how the values on the
sides of the triangle "pair up". The
h
pairs with the 15, the
o
pairs with the x, but the
a
stands alone. The a has no companion term. This means
that the a is NOT involved
in the solution of this problem. Cross it out!
 This problem deals with o
and h which means it is
using sin A.

ANSWER: 8.6

Set
Up the Formula:
 Place
the degrees in the formula for angle A.
 Replace
o
and
h
with their companion terms.
 Using
your scientific/graphing calculator, determine the value of the left
side of the equation.
(On most scientific calculators,
press 35 first and then press the
sin
key.
On
most graphing calculators, press the sin
key first and the 35 second.)
 Solve
the equation algebraically. In this case, cross multiply and solve for
x. Or just remember that if the x is on
the top, you will multiply to arrive at your answer. If
x is on the bottom, divide to arrive at your answer (see
next example).
 Round
answer to the desired value.

Example 2: In
right triangle ABC, leg length BC=20 and angle
B = 41º.
Find hypotenuse length BA to the nearest hundredth.
Set up the diagram and the formula in the same
manner as was done in Example 1. You should arrive at the
drawing and the formula shown here. 


Hint:
If you are having a problem solving the equation
algebraically, remember that when x is on the bottom, you
must divide to arrive at your answer. The division is always
"divide BY the trig value decimal". 
Hint:
Be sure your answer MAKES SENSE!!! The hypotenuse is always
the largest side in a right triangle. So, our answer of
26.50 makes sense  it is bigger than the leg of 20. 
You really know a
lot of facts about these triangles:

See how to use
your
TI83+/TI84+ graphing calculator with
beginning trigonometry.
Click calculator. 


