Most problems in trigonometry involve finding the length of an
unknown side of a triangle when given one angle and one side or finding an
unknown angle in a triangle when the lengths of two sides are given. The
solution procedure is always the same:
• Sketch the triangle.
• Identify the known and unknown
quantities and show on the sketch.
• Decide which trigonometric
function to use.
• Set up an equation using a
trigonometric function.
• Solve the equation for the
unknown quantity.
The next examples illustrate how to solve for sides of a
triangle using trigonometric functions
EXAMPLE 20.4A:
Solving a Right Triangle
For the triangle shown in Figure 20.17, solve for
∠
B
and the lengths of sides
a
and
c
.
FIGURE 20.17
Solution:
STEP 1:
Find
∠
B
Since the sum of the angle measures of a triangle must add to
180, the measure of
∠
B
is:
m
∠
B
= 180 – 90 – 28 = 62°
So,
∠
B
= 62°.
STEP 2:
Find
side
a
The length of side
a
can
be solved using either
∠
A
or
∠
B
as
a reference. If we choose
∠
A
, then the adjacent side is the
known side and the opposite side is the unknown side. This means that we can
use the tangent function by writing: