8-2
8-2 Trigonometric
TrigonometricRatios
Ratios
HoltMcDougal
GeometryGeometry
Holt
8-2 Trigonometric Ratios
Warm Up
Write each fraction as a decimal
rounded to the nearest hundredth.
1.
2.
Solve each equation.
3.
Holt McDougal Geometry
4.
8-2 Trigonometric Ratios
Holt McDougal 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 sine of A is written
as sin A.
Holt McDougal Geometry
8-2 Trigonometric Ratios
Write the trigonometric ratio as a fraction and
as a decimal rounded to the nearest
hundredth.
Holt McDougal Geometry
8-2 Trigonometric Ratios
Write the trigonometric ratio as a fraction and
as a decimal rounded to
the nearest hundredth.
Holt McDougal Geometry
8-2 Trigonometric Ratios
Use your calculator to find the trigonometric
ratio. Round to the nearest hundredth.
sin 52°
Holt McDougal Geometry
Caution!
Be sure your
calculator is in
degree mode, not
radian mode.
8-2 Trigonometric Ratios
Steps for using trigonometric ratios.
1. Circle ONE angle.
2. Label Opposite, adjacent, or hypotenuse.
3. Use SOHCAHTOA
Holt McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest
hundredth.
BC
Holt McDougal 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 McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest hundredth.
QR
Holt McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest hundredth.
FD
Holt McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest
hundredth.
DF
Holt McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest hundredth.
ST
Holt McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest hundredth.
BC
Holt McDougal Geometry
8-2 Trigonometric Ratios
Find the length. Round to the nearest
hundredth.
JL
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Holt McDougal Geometry
8-2 Trigonometric Ratios
Example 5: Problem-Solving Application
The Pilatusbahn in Switzerland is the world’s steepest cog
railway. Its steepest section makes an angle of about 25.6º with
the horizontal and rises about 0.9 km. To the nearest hundredth
of a kilometer, how long is this section of the railway track?
Holt McDougal Geometry
8-2 Trigonometric Ratios
A flagpole is held upright by 30m long wires to the
ground. If the wires make an angle of 25 degrees
to the ground, how high is the flagpole?
Holt McDougal Geometry
8-2 Trigonometric Ratios
A surveyor wants to the measure the width of a
river at point A. She places stakes 100 feet apart
on the far side of the river and she is standing at
point A. She finds that the measurement of angle
BAC is 27 degrees and ABC is 90 degrees. How
wide is the river?
Holt McDougal Geometry
8-2 Trigonometric Ratios
Lesson Quiz: Part I
Use a special right triangle to write each
trigonometric ratio as a fraction.
1. sin 60°
2. cos 45°
Use your calculator to find each
trigonometric ratio. Round to the nearest
hundredth.
3. tan 84°
Holt McDougal Geometry
4. cos 13°
8-2 Trigonometric Ratios
Lesson Quiz: Part II
Find each length. Round to the nearest
tenth.
5. CB
6. AC
Use your answers from Items 5 and 6 to
write each trigonometric ratio as a fraction
and as a decimal rounded to the nearest
hundredth.
7. sin A
Holt McDougal Geometry
8. cos A
9. tan A