Section 7.1 Solving Right Triangles
This sections gives examples that show how to solve for various parts of right triangles, given suﬃcient
information about the triangle.
Pythagorean Theorem:
A triangle with sides
a
,
b
,
c
is a right triangle iﬀ
c
2
=
a
2
+
b
2
.
Example.
If
b
=4,
α
=10
o
in the above triangle, ﬁnd
a
,
c
,
β
.
Solution. tan
α
=
a
b
a
=
b
tan
α
=4tan10
o
≈
.
7053
c
2
=
a
2
+
b
2
=
.
7053
2
+4
2
=16
.
497
c
=4
.
06
α
+
β
=90
o
implies
β
=90
o

α
=90
o

10
o
=80
o
Example.
Let
c
= 10,
α
=40
o
in the above triangle. Find
b
,
a
,
β
.
Solution. Since
α
=40
o
,
β
=90
o

40
o
=50
o
.
sin
β
=
b
c
=
b
10
implies
b
=10sin
β
=10s
in50
o
=7
.
66
cos
β
=
a
c
=
a
10
implies
a
=10cos
β
= 10 cos50
o
=6
.
43.
Example.
One angle of a right triangle is
π
8
radians and one leg is 3 meters. Find the length of the
hypotenuse
c
.
Solution.
Case 1. The side adjacent to the
π
8
angle is 3.
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 Fall '11
 Kutter
 Algebra, Angles, Pythagorean Theorem, Right triangle, Hypotenuse, triangle, β

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