Applications and Solving Right Triangles
•
Section 1.3
19
θ
r
cos
θ
r
sin
θ
r
For some problems it may help to remember that when a right tri
angle has a hypotenuse of length
r
and an acute angle
θ
, as in the
picture on the right, the adjacent side will have length
r
cos
θ
and the
opposite side will have length
r
sin
θ
. You can think of those lengths
as the horizontal and vertical “components” of the hypotenuse.
Notice in the above right triangle that we were given two pieces of information: one of
the acute angles and the length of the hypotenuse. From this we determined the lengths of
the other two sides, and the other acute angle is just the complement of the known acute
angle. In general, a triangle has six parts: three sides and three angles.
Solving a triangle
means ±nding the unknown parts based on the known parts. In the case of a right triangle,
one part is always known: one of the angles is 90
◦
.
Example 1.19
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 Fall '11
 Dr.Cheun
 Calculus, Trigonometry, Angles, Pythagorean Theorem, Law Of Cosines, Right triangle, Hypotenuse, triangle

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