Download trigonometric ratio

8-2
8-2 Trigonometric
TrigonometricRatios
Ratios
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
8-2 Trigonometric Ratios
Warm Up
Write each fraction as a decimal
rounded to the nearest hundredth.
1.
2.
0.67
0.29
Solve each equation.
3.
Holt Geometry
x = 7.25
4.
x = 7.99
8-2 Trigonometric Ratios
Objectives
Find the tangent of an acute angle.
Use trigonometric ratios to find side
lengths and angles in right triangles.
Holt Geometry
8-2 Trigonometric Ratios
Vocabulary
trigonometric ratio
tangent
Holt Geometry
8-2 Trigonometric Ratios
By the AA Similarity Postulate, a right triangle with
a given acute angle is similar to every other right
triangle with that same acute angle measure. So
∆ABC ~ ∆DEF ~ ∆XYZ, and
. These are
trigonometric ratios. A trigonometric ratio is a ratio
of two sides of a right triangle.
Holt Geometry
8-2 Trigonometric Ratios
Note 66
Holt Geometry
8-2 Trigonometric Ratios
Writing Math
In trigonometry, the letter of the vertex of the
angle is often used to represent the measure of
that angle. For example, the tangent of A is
written as tan A.
Holt Geometry
8-2 Trigonometric Ratios
Example 1A: Finding Trigonometric Ratios
Write the trigonometric
ratio as a fraction and
as a decimal rounded to
the nearest hundredth.
tan J
Holt Geometry
8-2 Trigonometric Ratios
Example 1B: Finding Trigonometric Ratios
Write the trigonometric
ratio as a fraction and
as a decimal rounded to
the nearest hundredth.
Tan K
Holt Geometry
8-2 Trigonometric Ratios
Example 2: Finding Trigonometric Ratios in Special
Right Triangles
Use a special right triangle to write tan 30°
as a fraction.
Holt Geometry
8-2 Trigonometric Ratios
Check It Out! Example 2
Use a special right triangle to write tan 45°
as a fraction.
45°
s
45°
s
Holt Geometry
8-2 Trigonometric Ratios
Example 3C: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric
ratio. Round to the nearest hundredth.
tan 65°
Caution!
Be sure your
calculator is in
degree mode, not
radian mode.
tan 65°  2.14
Holt Geometry
8-2 Trigonometric Ratios
Check It Out! Example 3a
Use your calculator to find the trigonometric
ratio. Round to the nearest hundredth.
tan 11°
tan 11°  0.19
Holt Geometry
8-2 Trigonometric Ratios
Example 4A: Using Trigonometric Ratios to Find
Lengths
Find the length. Round to
the nearest hundredth.
BC
Holt Geometry
8-2 Trigonometric Ratios
Caution!
Do not round until the final step of your answer.
Use the values of the trigonometric ratios
provided by your calculator.
Holt Geometry
8-2 Trigonometric Ratios
Example 4C: Using Trigonometric Ratios to Find
Lengths
Find the length and the missing
angle. Round to the nearest
hundredth.
ED
D
Holt Geometry
8-2 Trigonometric Ratios
Check It Out! Example 4c
Find the length and the
missing angle. Round to
the nearest hundredth.
BC
A
Holt Geometry
8-2 Trigonometric Ratios
Exit Slip
Use a special right triangle to write each
trigonometric ratio as a fraction.
1. tan 60°
2. tan 45°
Use your calculator to find each
trigonometric ratio. Round to the nearest
hundredth.
3. tan 84°
Find each length. Round
to the nearest tenth.
4. CB
Holt Geometry