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8.3 Tangent Ratio 1 March 04, 2010 Feb 238:28 AM 8.3: Tangent Ratio Objective: Use the tangent ratio to determine side lengths in right triangles.

# 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3 Tangent Ratio 10 March 04, 2010 Feb 249:53 PM The inverse of the tangent ratio If

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### Text of 8.3 Tangent Ratio - Poudre School Districtstaffweb.psdschools.org/kemotich/Mrs_Motichka... · 8.3... 8.3 Tangent Ratio

1

March 04, 2010

Feb 23­8:28 AM

8.3: Tangent Ratio

Objective:  Use the tangent ratio to determine side lengths in right triangles. 8.3 Tangent Ratio

2

March 04, 2010

Feb 24­11:37 AM

For each triangle identify the length of the hypotenuse, the length of the side opposite angle B, and the length of the side adjacent to angle B. 8.3 Tangent Ratio

3

March 04, 2010

Feb 24­11:47 AM

36.87o

53.13o

6

8

10

36.87o

53.13o

9

12

15

36.87o

53.13o

UVTV

=

TVUV

=

UVTV

=

TVUV

=

UVTV

=

TVUV

= 8.3 Tangent Ratio

4

March 04, 2010

Feb 24­11:49 AM

tan (      ) = A

B

A C

Leg opposite     A

For each pair of complementary angles,        and        , there is a family of similar right triangles.  In each such family, the tangent ratio is constant no matter the size of     ABC.

A B

tan (      ) = B

What is the tangent of     B in the above diagram? 8.3 Tangent Ratio

5

March 04, 2010

Feb 24­7:24 PM

Write the tangent ratio for     T and     U.

Step 1:  Identify the opposite and adjacent sides from the angle.

Step 2:  Write the tangent ratio. 8.3 Tangent Ratio

6

March 04, 2010

Feb 24­7:42 PM

We can also use the tangent ratio to find the side lengths of right triangles.

Ex)  Find the value of w to the nearest tenth.

Step 1:  Identify the opposite and adjacent sides from the angle.

Step 2:  Write the tangent ratio and solve for w.

Step 3:  Get your handy­dandy calculator and plug it in. 8.3 Tangent Ratio

7

March 04, 2010

Feb 24­7:42 PM

We can also use the tangent ratio to find the side lengths of right triangles.

Ex)  Find the value of w to the nearest tenth.

Step 1:  Identify the opposite and adjacent sides from the angle.

Step 2:  Write the tangent ratio and solve for w.

Step 3:  Get your handy­dandy calculator and plug it in. 8.3 Tangent Ratio

8

March 04, 2010

Feb 24­7:49 PM

People actually use this stuff!!!!(Can you believe it?)

The tangent ratio can be used to measure distances that would be difficult to measure directly.

For instance:  The distance from the earth to the moon and any other celestial body we can see. 8.3 Tangent Ratio

9

March 04, 2010

Feb 24­8:58 PM

Let us try it:  Find the distance from the earth to the moon.drawing not to scale

0.955o

3,950 mi

x

Average distance from the earth to the moon:  238,855 mi 8.3 Tangent Ratio

10

March 04, 2010

Feb 24­9:53 PM

The inverse of the tangent ratioIf we know the tangent ratio, we can also use the inverse of tangent to find the angle measure.

Ex)  Find the value of x to the nearest degree.

Step 1:  Identify the opposite and adjacent sides from the angle.

Step 2:  Write the tangent ratio.

Step 3:  Get your handy­dandy calculator and plug it in. 8.3 Tangent Ratio

11

March 04, 2010

Feb 24­9:53 PM

The inverse of the tangent ratioIf we know the tangent ratio, we can also use the inverse of tangent to find the angle measure.

Ex)  Find the value of x to the nearest degree.

Step 1:  Identify the opposite and adjacent sides from the angle.

Step 2:  Write the tangent ratio.

Step 3:  Get your handy­dandy calculator and plug it in. 8.3 Tangent Ratio

12

March 04, 2010

Feb 24­10:09 PM

Homework

Pg. 434# 1 ­ 9 odd, 11 ­ 15 odd,

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