Download PP Section 9.4

Geometry Sections 9.4 & 9.5
Trigonometric Ratios
What you will learn:
1. Use the tangent, sine and cosine ratios
2. Solve real-life problems involving these
ratios
The word “trigonometry” comes from two Greek
words which mean triangle measurement. And
that is exactly what we will do with trigonometry we will find the measures of angles and the length
of sides in triangles. In sections 9.4 - 9.6, we will
limit ourselves to right triangles. In section 9.7,
we will look at trigonometry for non-right
triangles.
A trigonometric ratio (i.e. fraction) is a ratio of
the lengths of two sides of a right triangle.
The three basic trigonometric ratios are sine
(______),
sin cosine (______)
cos and tangent
(______).
tan These ratios are defined for the
acute angles of a right triangle as follows.
opposite leg
hypotenuse
adjacent leg
hypotenuse
opposite leg
adjacent leg
adjacent
leg
hypotenuse
opposite leg
An easy way to remember these three trig
ratios is with the mnemonic
SOH  CAH  TOA
Example: Write the correct ratio for each trigonometric
ratio.
3
4
5
5
4
5
3
5
3
4
4
3
Sine and Cosine of complementary angles:
The sine of an angle is equal to the cosine of
its complement.
The cosine of an angle is equal to the sine of
its complement.
Example:
Write sin28 in terms of cosine.
sin 28  cos 62
90  28
Write cos48 in terms of sine.
cos 48  sin 42
The value of the sine, cosine and tangent of
an angle depend only upon the measure of
the angle and not the size of the triangle that
the angle is found in. A scientific calculator
can be used to find the value of these three
trig ratios. Make sure your calculator is in
degree mode.
sin
0
13
.2250
= ___________
.2250
cos 770 = ____________
tan 400 = ____________
.8391
We can use the trig ratios to find the lengths
of unknown sides in right triangles.
Example: Solve for x and y. Round your answers to the
nearest 1000th.
adj
hyp
opp
hyp
adj
sin 28 
opp
12
x
x sin 28  12
12
x
 25.561
sin 28
12
tan 28 
y
y tan 28  12
12
y
 22.569
tan 28
x
cos 40 
20
20 cos 40  x
x  15.321
sin 40 
y
20
20 sin 40  y
y  12.856
Example: The angle of elevation to the top of a tree
from a point 100 feet from the base of the tree is 510.
Estimate the height of the tree to the nearest 1000th.
Note : The angle of elevation is the angle formed by the
line of sight up to some object and a horizontal line
x
tan 51 
100
opp
100 tan 51  x
x  123.490
adj
Example: A support wire for a tall radio tower is 280 ft.
long and is attached to the tower at a point exactly half
way up the tower. If the wire makes an angle of 64o
with the ground, find the height of the tower to the
nearest 1000th of a foot.
x
sin 64 
280
280 sin 64  x
x  251.662  2  503.324
hyp
opp
HW: pp491-492 / 5-10, 15-17
HW: pp498-499 / 7-8, 11- 14, 19-22, 27, 39, 30