Transcript Glencoe Geometry

• Trigonometry--The study of the properties of
triangles. Trigonometry means angle
measurement.
• Trigonometric Ratio--The ratios of the
measures of two sides of a right triangle.
Find Sine, Cosine, and Tangent Ratios
A. Express sin L as a
fraction and as a decimal to
the nearest hundredth.
Answer:
Find Sine, Cosine, and Tangent Ratios
B. Express cos L as a
fraction and as a decimal
to the nearest hundredth.
Answer:
Find Sine, Cosine, and Tangent Ratios
C. Express tan L as a
fraction and as a decimal
to the nearest hundredth.
Answer:
Find Sine, Cosine, and Tangent Ratios
D. Express sin N as a
fraction and as a decimal
to the nearest hundredth.
Answer:
Find Sine, Cosine, and Tangent Ratios
E. Express cos N as a
fraction and as a decimal to
the nearest hundredth.
Answer:
Find Sine, Cosine, and Tangent Ratios
F. Express tan N as a
fraction and as a decimal to
the nearest hundredth.
Answer:
A. Find sin A.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
B. Find cos A.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
C. Find tan A.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
D. Find sin B.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
E. Find cos B.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
F. Find tan B.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
Use Special Right Triangles to Find
Trigonometric Ratios
Use a special right triangle to express the cosine of
60° as a fraction and as a decimal to the nearest
hundredth.
Draw and label the side lengths of a
30°-60°-90° right triangle, with x as
the length of the shorter leg and 2x
as the length of the hypotenuse.
The side adjacent to the 60° angle
has a measure of x.
Use Special Right Triangles to Find
Trigonometric Ratios
Definition of cosine ratio
Substitution
Simplify.
Use a special right triangle to express the tangent
of 60° as a fraction and as a decimal to the nearest
hundredth.
A.
B.
C.
D.
A.
B.
C.
D.
A
B
C
D
Estimate Measures Using
Trigonometry
EXERCISING A fitness trainer sets the incline on a
treadmill to 7°. 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.
Estimate Measures Using
Trigonometry
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 4.8°, about how high
does the ramp rise off the ground to the nearest
inch?
A. 1 in.
B. 11 in.
C. 16 in.
D. 15 in.
A.
B.
C.
D.
A
B
C
D
Find Angle Measures Using Inverse
Trigonometric Ratios
Use a calculator to find the measure of P to the
nearest tenth.
Find Angle Measures Using Inverse
Trigonometric Ratios
The measures given are those of the leg adjacent to P
and the hypotenuse, so write the equation using the
cosine ratio.
KEYSTROKES: 2nd [COS] ( 13 ÷ 19 )
ENTER 46.82644889
Answer: So, the measure of P is approximately 46.8°.
Use a calculator to find the measure of D to the
nearest tenth.
A. 44.1°
B. 48.3°
C. 55.4°
D. 57.2°
A.
B.
C.
D.
A
B
C
D
Solve a Right Triangle
Solve the right triangle. Round side measures to
the nearest hundredth and angle measures to the
nearest degree.
Solve a Right Triangle
Step 1
Find mA by using a tangent ratio.
Definition of inverse
tangent
29.7448813 ≈ mA
Use a calculator.
So, the measure of A is about 30.
Solve a Right Triangle
Step 2
Find mB using complementary angles.
mA + mB = 90
30 + mB ≈ 90
mB ≈ 60
Definition of
complementary
angles
mA ≈ 30
Subtract 30 from
each side.
So, the measure of B is about 60.
Solve a Right Triangle
Step 3
Find AB by using the Pythagorean Theorem.
(AC)2 + (BC)2 = (AB)2
Pythagorean Theorem
72 + 42
= (AB)2
Substitution
65
= (AB)2
Simplify.
Take the positive
square root of each
side.
8.06
≈ AB
Use a calculator.
Solve a Right Triangle
So, the measure of AB is about 8.06.
Answer: mA ≈ 30, mB ≈ 60, AB ≈ 8.06
Solve the right triangle. Round side measures to
the nearest tenth and angle measures to the
nearest degree.
A. mA = 36°, mB = 54°,
AB = 13.6
B. mA = 54°, mB = 36°,
AB = 13.6
C. mA = 36°, mB = 54°,
AB = 16.3
D. mA = 54°, mB = 36°,
AB = 16.3
A.
B.
C.
D.
A
B
C
D
• Summary:
– If you are given the angle, use sin,
cos, and tan
– If you want to find the angle, use sin-1,
cos-1, and tan-1