Trigonometric Ratios - Murphymath
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1
2
3Trigonometric Ratios
o
o
o
A. An Introduction to Trigonometric Ratios with 30
-60
-90
Triangles
1. Fill in ALL the missing side lengths in the triangles below:
Triangle #1
Triangle #2
Triangle #3
4
o
o
o
60
60
60
1
o
o
o
30
30
30
5
3
o
2. Now fill in the numbers for the following ratios, using the 30
angle in each triangle
above as your reference angle. (It may help to imagine that you are standing at the vertex
o
of the 30
angle in each triangle as you fill in the chart.) Write your answers in simplest
radical form (rationalize the denominators).
o
In relation to the 30
Angle:
Triangle #1
Triangle #2
Triangle #3
Opposite
Leg
Hypotenuse
Adjacent
Leg
Hypotenuse
Opposite
Leg
Adjacent
Leg
3. What do you notice about the ratios within any given row of the chart?
___________________________
When right triangles are similar, the above ratios remain constant for ANY given acute
o
o
o
reference angle of ANY right triangle (not just 30
-60
-90
triangles). If we were to
o
o
o
know all three side lengths of three similar 37
-53
-90
triangles (whose lengths are not
o
so obvious and quick to compute!) and complete the above chart, say, for the 53
angle in
each triangle, we would still find that each row of the chart would give a constant ratio.
Because these ratios are constant, they are a useful tool for finding missing angles and
sides of right triangles (and countless other applications as well). These ratios are the
basic Trigonometric ratios, and are defined below.
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