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
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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
Leg adjacent to 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,
22 and 31
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