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Chapter 4: D. Basic Trigonometry 33
where x is the value of the trigonometric function. Each inverse function returns
the angle measure associated with the value x. For example, given that sin(A) =
0.4580, we can find the angle A in degrees using a scientific calculator:
OBLIQUE TRIANGLES
A = sin –1 (0.4580) = 27.26°
An oblique triangle has no 90-degree angles. Some special types of oblique triangles
include the equilateral triangle, isosceles triangle, and the scalene triangle, shown
in Table 4.3.
Part I.D
SOLVING OBLIQUE TRIANGLES
Each triangle has three sides and three angles. In order to solve for an unknown
side or angle in an oblique triangle, three pieces of information must be known. We
will use the laws of sines and cosines to solve these problems.
Law of Sines
Given an oblique triangle such as the one in Figure 4.3, the law of sines states
( ) =
( ) =
( )
sin X sin Y sin Z
.
x y z
Table 4.3 Oblique triangles.
Triangle type
Example
Equilateral triangle
Three equal sides,
three 60° angles
s
60°
s
60°
60°
s
Isosceles triangle
Two equal sides,
two equal angles
s
s
Scalene triangle
All sides, all
angles unique
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