Transcript Trigonometric Ratios

7.4 Trigonometry

Find trigonometric ratios using right
triangles

Solve problems using trigonometric ratios
The word trigonometry originates from
two Greek terms, trigon, which means
triangle, and metron, which means
measure. Thus, the study of trigonometry
is the study of triangle measurements.
 A ratio of the lengths of the sides of a
right triangle is called a trigonometric
ratio. The three most common
trigonometric ratios are sine, cosine, and
tangent.

For right ∆ABC…



sin A = opposite side = a
hypotenuse
c
A
c
b
cos A = adjacent side = b
hypotenuse
c
tan A = opposite side = a
adjacent side b
C
a
B
To help you remember
A
these trigonometric
Sin Arelationships,
= Opposite side youSOH
can
Hypotenuse
use the mnemonic
Cos A
= Adjacent
side
CAH
device,
SOH-CAH-TOA,
b
Hypotenuse
where the first letter of
Tan A
= Opposite
side
each
word
of theTOA
Adjacent side
trigonometric ratios is
C
represented in the
correct order.
c
a
B
Find sin L, cos L, tan L, sin N, cos N, and tan N.
Express each ratio as a fraction and as a decimal.
Answer:
Find sin A, cos A, tan A, sin B, cos B, and tan B.
Express each ratio as a fraction and as a decimal.
Answer:
Use a calculator to find tan
thousandth.
KEYSTROKES: TAN
Answer:
56
to the nearest ten
ENTER
1.482560969
Use a calculator to find cos
thousandth.
KEYSTROKES: COS
Answer:
90
to the nearest ten
ENTER
0
a. Use a calculator to find sin 48° to the nearest ten
thousandth.
Answer:
b. Use a calculator to find cos 85° to the nearest ten
thousandth.
Answer:

You can use a calculator or a
trigonometric table to find the missing
measures of a right triangle if you are
given the measures of two sides of the
triangle or one side and one acute
angle.
EXERCISING A fitness trainer sets the incline on a
treadmill to
The walking surface is 5 feet long.
Approximately how many inches did the trainer raise
the end of the treadmill from the floor?
Let y be the height of the treadmill from the floor in inches.
The length of the treadmill is 5 feet, or 60 inches.
Multiply each side by 60.
Use a calculator to find y.
KEYSTROKES: 60
SIN
7
ENTER
7.312160604
Answer: The treadmill is about 7.3 inches high.
CONSTRUCTION The bottom of a handicap ramp is
15 feet from the entrance of a building. If the angle of
the ramp is about
how high does the ramp rise
off the ground to the nearest inch?
Answer: about 15 in.
COORDINATE GEOMETRY Find mX in right XYZ for
X(–2, 8), Y(–6, 4), and Z(–3, 1).
Explore You know the coordinates of the vertices of a
right triangle and that
is the right angle. You
need to find the measures of one of the angles.
Plan
Use the Distance Formula to find the measure
of each side. Then use one of the trigonometric
ratios to write an equation. Use the inverse to
find
Solve
or
or
or
Use the cosine ratio.
Simplify.
Solve for x.
Use a calculator to find
KEYSTROKES:
2ND
4
ENTER
Examine Use the sine ratio to check the answer.
Simplify.
5
)
KEYSTROKES:
2ND
ENTER
Answer: The measure of
is about 36.9.
3
5
)
COORDINATE GEOMETRY
Answer: about 56.3

Pre-AP Geometry:
Pg. 368 #18 – 48,
50, 51, 56 – 58

Geometry:
Pg. 368 #18 – 48