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Five-Minute Check (over Lesson 8–3)
CCSS
Then/Now
New Vocabulary
Key Concept: Trigonometric Ratios
Example 1: Find Sine, Cosine, and Tangent Ratios
Example 2: Use Special Right Triangles to Find Trigonometric
Ratios
Example 3: Real-World Example: Estimate Measures Using
Trigonometry
Key Concept: Inverse Trigonometric Ratios
Example 4: Find Angle Measures Using Inverse Trigonometric
Ratios
Example 5: Solve a Right Triangle
Content Standards
G.SRT.6 Understand that by similarity, side ratios in
right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios
for acute angles.
G.SRT.7 Explain and use the relationship between
the sine and cosine of complementary angles.
Mathematical Practices
1 Make sense of problems and persevere in solving
them.
5 Use appropriate tools strategically.
You used the Pythagorean Theorem to find
missing lengths in right triangles.
•  Find trigonometric ratios using right triangles.
•  Use trigonometric ratios to find angle
measures in right triangles.
•  trigonometry
•  trigonometric ratio
•  sine
•  cosine
•  tangent
•  inverse sine
•  inverse cosine
•  inverse tangent
Find Sine, Cosine, and Tangent Ratios
A. Express sin L as a
fraction and as a decimal to
the nearest hundredth.
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.
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.
B. Find cos A.
C. Find tan A.
D. Find sin B.
E. Find cos B.
F. Find tan B.
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.
Use a special right triangle to express the tangent
of 60° as a fraction and as a decimal to the nearest
hundredth.
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?
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.
Find Angle Measures Using Inverse
Trigonometric Ratios
Use a calculator to find the measure of !P to the
nearest tenth.
Use a calculator to find the measure of !D to the
nearest tenth.
Solve a Right Triangle
Solve the right triangle. Round side measures to
the nearest hundredth and angle measures to the
nearest degree.
8.4 HW:
P. 573
16-44E, 70-78E