Pre-Algebra Chapter 9

Sine, Cosine, and
Tangent Ratios
Vocabulary
• trigonometry
• trigonometric ratio
• sine
• cosine
• tangent
• Find sine, cosine, and tangent ratios.
• Solve problems by using the trigonometric ratios.
are ratios in right triangles used in the real world?
In parasailing, a towrope is
used to attach the parachute
to the boat.
a. What type of triangle do
the towrope, water, and
A
height of the person above
the water form?
b. Name the hypotenuse
B
C
of the triangle.
c. What type of angle do the towrope and the water form?
d. Which side is opposite this angle?
e. Other than the hypotenuse, name the side adjacent to this angle.
FIND TRIGONOMETRIC RATIOS Trigonometry is the study of the
properties of triangles. The word trigonometry means angle measure. A
trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
Reading Math
Trigonometry Terms
The notation sin A is read the sine
of angle A. The notation cos A is
read the cosine of angle A. The
notation tan A is read the tangent
of angle A.
The most common trigonometric ratios are the sine, cosine, and tangent
ratios. These ratios are abbreviated as sin, cos, and tan, respectively.
• Words
If A is an acute angle of a right triangle,
measure of leg opposite A
sin A ,
measure of hypotenuse
measure of leg adjacent to A
cos A , and
measure of hypotenuse
measure of leg opposite A
tan A .
measure of leg adjacent to A
Trigonometric Ratios
• Model B
• Symbols sin A a c
leg
opposite
A
a
C
b
leg adjacent to
hypotenuse
c
A
A
cos A b c
tan A b
a
All right triangles that have the same measure for A are similar. So, the
value of the trigonometric ratio depends only on the measure of A, not the
size of the triangle. The trigonometric ratios are the same for angle A no
matter what the size of the triangle.
Lesson 9-8 Sine, Cosine, and Tangent Ratios 477