Right Triangle Trigonometry
In this section, we are interested in using trigonometric functions to compute the values of all
angles and sides of any right triangle, given the value of any two sides of the triangle or the value
of one side and one acute angle. This process is called “solving the right triangle.”
Consider the right triangle shown below, where angle
θ
is one of the acute angles. We may
define the functions in terms of the hypotenuse (Hyp), the side adjacent (Adj) to angle
θ
, and the
side opposite (Opp) the angle
θ
for any right triangle, as shown below.
sin
cos
tan
Opp
Hyp
Adj
Hyp
Opp
Adj
θ
θ
θ
=
=
=
csc
sec
cot
Hyp
Opp
Hyp
Adj
Adj
Opp
θ
θ
θ
=
=
=
In order to solve right triangles given the lengths of two sides or one side and the value of one
acute angle, it will be necessary to compute the value of a trigonometric function of one of the
angles. We can use a calculator to do this.
We may also need a calculator to compute the value of an inverse trigonometric function, that is,
the value of an angle given the value of a trigonometric function of that angle. The inverse
function of a sine function, for example, can be written as sin-1 or as arcsin.
To illustrate, we may remember that
()
3
sin 60 2
°= . So for the inverse function, we may write
13
sin 60
2
−=°, or 3
arcsin 60
2=°.
