- By
**pier** - Follow User

- 60 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Bell Ringer' - pier

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Tangent Ratios

- A trigonometric ratios is a ratio of the lengths of two sides of a right triangle.
- For any acute angle of a right triangle, there is a leg opposite the angle and a leg adjacent to the angle. The ratio of these legs is the tangent of the angle.

SOLUTION

leg opposite S

4

tan S =

=

=

≈ 1.7321

4

leg adjacent to S

leg opposite R

1

4

3

3

3

3

=

=

tan R =

≈ 0.5774

leg adjacent to R

4

Find Tangent Ratio

Find tan S and tan R as fractions in simplified form and as decimals rounded to four decimal places.

SOLUTION

Rounded value

Calculator keystrokes

Display

3.487414444

3.4874

Use a Calculator for Tangent

Approximate tan74° to four decimal places.

or

74

74

Find Tangent Ratio

Find tan Sand tan R as fractions in simplified form and as decimals. Round to four decimal places if necessary.

1.

tan S =

tan R =

≈1.3333

=0.75;

ANSWER

12

3

4

5

=2.4

tan S =

tan R =

≈0.4167;

12

3

4

5

ANSWER

2.

Now you Try

Find Tangent Ratio

Use a calculator to approximate the value to four decimal places.

3.

tan 35°

4.

tan 85°

11.4301

0.7002

0.1763

ANSWER

ANSWER

ANSWER

5.

tan 10°

Find Leg Length

Use a tangent ratio to find the value of x. Round your answer to the nearest tenth.

SOLUTION

tan 22° =

Write the tangent ratio.

Substitute.

3

tan 22° =

x

opposite leg

x· tan 22° = 3

Multiply each side by x.

adjacent leg

Divide each side by tan22°.

x =

3

Use a calculator or table to approximate tan22°.

tan 22°

x ≈

3

x≈ 7.4

Simplify.

0.4040

Method 1

Method 2

Find Leg Length

Use two different tangent ratios to find the value of x to the nearest tenth.

SOLUTION

First, find the measure of the other acute angle: 90° – 35° = 55°.

tan 55° =

tan 35° =

x

4

tan 55° =

tan 35° =

x

4

opposite leg

opposite leg

adjacent leg

adjacent leg

x· tan 35° = 4

4 tan 55° = x

Find Leg Length

4(1.4281)≈x

x≈ 5.7

x≈ 5.7

The two methods yield the same answer: x≈5.7.

ANSWER

x =

4

tan 35°

x ≈

4

0.7002

Estimate Height

You stand 45 feet from the base of a tree and look up at the top of the tree as shown in the diagram. Use a tangent ratio to estimate the height of the tree to the nearest foot.

SOLUTION

tan 59° =

Write ratio.

h

tan 59° =

45

opposite leg

Substitute.

adjacent leg

45 tan 59° = h

Multiply each side by 45.

45(1.6643)≈h

Use a calculator or table to approximate tan 59°.

74.9≈h

Simplify.

ANSWER

8

tan 44° =

and

tan 46° =

x

Now you Try

Find Side Length

Write two equations you can use to find the value of x.

6.

ANSWER

x

4

5

x

x

7.

x

x

8

4

5

tan 37° =

and

tan 53° =

ANSWER

8.

tan 59° =

and

tan 31° =

Now you Try

Find Side Length

Find the value of x. Round your answer to the nearest tenth.

9.

10.

12.6

10.4

34.6

ANSWER

ANSWER

ANSWER

11.

Download Presentation

Connecting to Server..