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Chapter 4: D. Basic Trigonometry 31
B
a = 6
c
Part I.D
C
90°
b
49°
A
Figure 4.2 Finding angles in a right triangle.
side and one angle. For example, given that angle A is 49 degrees and side a has
length 6, angle B can be found, as well as the lengths of sides b and c, as shown in
Figure 4.2.
Finding the Unknown Angle
Since the angles of a triangle sum to 180 degrees, we can find the unknown angle
via subtraction. For example, given the triangle in Figure 4.2, we can find the
unknown angle B:
A+ B+ C = 180
49 + B + 90 = 180
139 + B = 180
B + 139 139 = 180 139
B =
Alternatively, using the fact that the two acute angles of a right triangle are complementary,
meaning that they sum to 90 degrees:
41
A+ B=
90
49 + B = 90
B + 49 49 = 90 49
B = 41
After finding all the angles, we can find the lengths of the unknown sides b and c.
Finding the Unknown Sides
We can find the lengths of the unknown sides using the trigonometric functions
and a calculator: