Download 9.5 Trigonometric Ratios

Warm-up

Find the value of each variable. Express your answer is
simplest radical form.
Classify a triangle with the given sides as acute, obtuse,
or right.
4. 6, 7, 10

SECTION 8.3 DAY 1:
TRIGONOMETRIC RATIOS
Goal: Find the sine, the cosine and the tangent of an
angle.
Trigonometry means
“triangle measurement”



We can use trigonometric ratios to find the lengths
of sides of right triangles.
A trig ratio is a ratio of the length of two sides.
The three basic trig ratios are sine, cosine, and
tangent, which are abbreviated sin, cos, and tan,
respectively.
Trigonometric Ratios



Which side is the hypotenuse?
Which side is the leg that is adjacent to angle A?
Which side is the leg that is opposite angle A?
Basic Trig Ratios

Sine ratio: ratio of the length of the opposite leg of a right
triangle to the length of the hypotenuse.
sin 

opposite
hypotenuse
Cosine ratio: ratio of the length of the adjacent leg to the length
of the hypotenuse.
adjacent
cos 
hypotenuse

Tangent ratio: ratio of the length of the opposite leg to the
length of the adjacent leg.
opposite
tan 
adjacent
Example

Find the sine, cosine, and
the tangent of P.

sin P =

cos P =

tan P =
One More Example 
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
Find the sine, cosine, and the tangent of the acute angles of
the triangle.
In other words, find the sin, cos, and tan of X and the sin, cos, and
tan of Y.
sin X =
sin Y =
cos X =
cos Y =
tan X =
tan Y =
Quick Questions…
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
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Given a right triangle, the hypotenuse is always
opposite what angle?
What do you need to know before determining which
side is opposite and which side is adjacent?
Once you know that information, how do you
determine which side is opposite and which side is
adjacent?
Quick Review
Table of Trig Ratios


Page 845 in your Geo Textbook!
If you don’t have a calculator to do this for you, you
will use this page to help you determine what the
sine, cosine and tangents are of certain angles.
Basic Trig Examples:
Find the value of the variable. Round to the nearest tenth.
s
4
x
36°
r
6
26°
y
Story Problem Example 1

It is known that a hill frequently used for sled riding has an
angle of elevation of 30 at it’s bottom. If the length of a
sledder’s ride is 52.6 feet, estimate the height of the hill.



Draw a diagram and fill in any known values.
Consider the info that is available and important.
 You are given an angle, and the hypotenuse, and you want to find the
side opposite the angle.
Decide which trig ratio is sensible to use.
 Sine uses both the opposite and the hypotenuse.
52.6 feet
h
30°
Sin 30° = h
52.6
=> 0.5 = h => 0.5·52.6 = h => 26.3 Feet
52.6
Story Problem Example 2

You are measuring the height of a flag pole. You stand
19 feet from the base of the pole. You measure the angle
of elevation from a point on the ground to the top of the
pole to be 64°. Estimate the height of the pole.
Homework 
Section 8.3 WS, Due Monday