§5-5 Solving Right Triangles
Solving right triangles: Find all unknown parts of a right triangle,
given the measure of two sides or the measure of one acute angle and a side.
a
b
c
α
β
Figure 1
Basic relations between the elements of the right triangle:
α+β= 90o, a2+b2=c2
Locate the right triangle in the first quadrant of a rectangular coordinate
system, we have following relations:
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6
a
b
c
0o< β < 90o
(a, b)
β
α
sin β=b
c
cos β=a
c
tan β=b
a
csc β=c
b
sec β=c
a
cot β=a
b
Figure 2
Side bis often referred to as the side opposite angle β,aas the side
adjacent to angle β, and cas the hypotenuse. Using these designations
for an arbitrary right triangle, we have the relations (Figure 2).
Example Solve the right triangle with c= 6.25 feet with β= 32.2o
Solution. Solve for α:α= 90o
−32.2o= 57.8o.
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