Download Geometry 9.10 Class Notes

9.10 Trigonometric Ratios
A
B
C
B
A
C
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1.Find the sine, cosine, and tangent of <A and <B in Δ ABC.
B
5
3
C
A
3
sin<A = 5
sin<B =
4
5
cos<A= 4
5
cos<B =
3
5
tan<A = 3
4
tan<B =
4
3
4
2.
Compare sin <A with sin <B
Compare cos <A with cos <B
Compare tan <A with tan <B
3.
Write a generalization that your answers to the problem
above suggest.
Conclusion:
The sine of an angle equals the
cosine of the complementary angle,
or the cosine of an angle equals the
sine of the complementary angle.
Also, the tangents of complementary
angles are reciprocals.
Angle of Elevation
An angle of elevation is the angle
formed from point P to point A.
PA (line of sight) and PH (horizontal
line) is called the angle of elevation.
A
H
A
P
H
P
Angle of depression
If you look down from point P
towards point B, the angle that PB
makes with PH is called the angle of
depression.
P
H
B
A
ATTENTION!
An angle of elevation or depression is
an angle between a LINE OF SIGHT
and the HORIZONTAL.
DO NOT USE THE VERTICAL!!!!!
For triangles other than the 30-6090, and 45-45-90, use the table on
page 424. What is the distance by land to the
ship?
H
28°
360m
C
S
X
Draw parallel lines from the ground. Remember alt int <‘s are
congruent.
<CSH = 28°
Thus: tan 28 ° = 360
x
0.5317 = 360
x
0.5317X = 360
X ≈ 677
The horizontal distance is about 677 m.
Use a calculator where necessary.
Look up tan 28 °
on the table,
page 424, and
plug it in to
solve.
Multiply both sides
by x
Divide by 0.5317